Find a set of parametric equations for the rectangular equation. $\begin{array} { l } t = 2 - x \\ y = 1 - 6 x ^ { 2 } \end{array}$

A) $x = - t + 2 , y = - 6 t ^ { 2 } + 24 t - 23$ B) $x = t + 2 , y = - 6 t ^ { 2 } + 24 t - 23$ C) $x = t - 2 , y = - 6 t ^ { 2 } + 24 t - 23$ D) $x = - t + 2 , y = - 6 t ^ { 2 } + 23 t - 24$ E) $x = t + 2 , y = - 24 t ^ { 2 } + 6 t + 23$ A) $x = - t + 2 , y = - 6 t ^ { 2 } + 24 t - 23$ B) $x = t + 2 , y = - 6 t ^ { 2 } + 24 t - 23$ C) $x = t - 2 , y = - 6 t ^ { 2 } + 24 t - 23$ D) $x = - t + 2 , y = - 6 t ^ { 2 } + 23 t - 24$ E) $x = t + 2 , y = - 24 t ^ { 2 } + 6 t + 23$

Exam 10: Topics In Analytic Geometry

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 5 inches

(Multiple Choice)

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Question 521

Select the graph of the equation. $r = 2 - \sin \left( \theta - \frac { \pi } { 4 } \right)$

(Multiple Choice)

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Question 522

Find a set of parametric equations for the rectangular equation. $t = 2 - x$ $y = x ^ { 2 } + 5$

(Multiple Choice)

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Question 523

Find the equation of the parabola so that its graph matches the description. $( y - 5 ) ^ { 2 } = 2 ( x + 1 )$ ; upper half of parabola

(Multiple Choice)

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Question 524

Identify the conic as a circle or an ellipse. $x ^ { 2 } + y ^ { 2 } - 3 x + 4 y - 2 = 0$

(Multiple Choice)

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Question 525

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $9 x ^ { 2 } + 36 y ^ { 2 } - 20 x + 256 y - 535 = 0$

(Multiple Choice)

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Question 526

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = \frac { 6 } { 5 } \quad\quad\quad x = -3$

(Multiple Choice)

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Question 527

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 3.5,1.62 )$

(Multiple Choice)

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Question 528

Select the curve represented by the parametric equations. x=|t-2| y=t+6

(Multiple Choice)

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Question 529

Find a set of parametric equations for the rectangular equation. t=2-x y=1-6

(Multiple Choice)

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Question 530

Find the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 100 } = 1$

(Multiple Choice)

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Question 531

Select the graph of degenerate conic. $y ^ { 2 } - 49 x ^ { 2 } = 0$

(Multiple Choice)

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Question 532

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point $( 3 , - 2 )$

(Multiple Choice)

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Question 533

Find the vertex, focus, and directrix of the parabola. $y ^ { 2 } = 10 x$

(Multiple Choice)

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Question 534

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point (2,4); horizontal axis

(Multiple Choice)

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Question 535

Find the standard form of the equation of the ellipse with the given characteristics. Center: $( 15,5 )$ ; a = 3b; Foci: $( 5,5 ) , ( 25,5 )$ , where a - thr semimajor axis, b - semiminor axis.

(Multiple Choice)

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Question 536

The first artificial satellite to orbit Earth was Sputnik I (launched by the former Soviet Union in 1957).Its highest point above Earths surface was 943 kilometers, and its lowest point was 211 kilometers (see figure).The center of Earth was at one focus of the elliptical orbit, and the radius of Earth is 6392 kilometers.Find the eccentricity of the orbit.Round your results to four decimal place. $The first artificial satellite to orbit Earth was Sputnik I (launched by the former Soviet Union in 1957).Its highest point above Earths surface was 943 kilometers, and its lowest point was 211 kilometers (see figure).The center of Earth was at one focus of the elliptical orbit, and the radius of Earth is 6392 kilometers.Find the eccentricity of the orbit.Round your results to four decimal place. x = 211 \mathrm {~km} , y = 943 \mathrm {~km}$ $x = 211 \mathrm {~km} , y = 943 \mathrm {~km}$

(Multiple Choice)

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Question 537

The Falls Incline Railway in Niagara Falls, Ontario, Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 170 feet long with a 40% uphill grade (see figure).Using the origin of a rectangular coordinate system as the base of the inclined plane, find the equation of the line that models the railway track. $a = 170$

(Multiple Choice)

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Question 538

Select the polar equation with graph.

(Multiple Choice)

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Question 539

Find an equation of the ellipse with vertices $( \pm 9,0 )$ and eccentricity $e = \frac { 3 } { 9 }$ .

(Multiple Choice)

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Question 540

Showing 521 - 540 of 556

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 5 inches

Select the graph of the equation. $r = 2 - \sin \left( \theta - \frac { \pi } { 4 } \right)$

Find a set of parametric equations for the rectangular equation. $t = 2 - x$ $y = x ^ { 2 } + 5$

Find the equation of the parabola so that its graph matches the description. $( y - 5 ) ^ { 2 } = 2 ( x + 1 )$ ; upper half of parabola

Identify the conic as a circle or an ellipse. $x ^ { 2 } + y ^ { 2 } - 3 x + 4 y - 2 = 0$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $9 x ^ { 2 } + 36 y ^ { 2 } - 20 x + 256 y - 535 = 0$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = \frac { 6 } { 5 } \quad\quad\quad x = -3$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 3.5,1.62 )$

Select the curve represented by the parametric equations. x=|t-2| y=t+6

Find a set of parametric equations for the rectangular equation. t=2-x y=1-6

Find the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 100 } = 1$

Select the graph of degenerate conic. $y ^ { 2 } - 49 x ^ { 2 } = 0$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point $( 3 , - 2 )$

Find the vertex, focus, and directrix of the parabola. $y ^ { 2 } = 10 x$

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point (2,4); horizontal axis

Find the standard form of the equation of the ellipse with the given characteristics. Center: $( 15,5 )$ ; a = 3b; Foci: $( 5,5 ) , ( 25,5 )$ , where a - thr semimajor axis, b - semiminor axis.

Select the polar equation with graph.

Find an equation of the ellipse with vertices $( \pm 9,0 )$ and eccentricity $e = \frac { 3 } { 9 }$ .

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 10: Topics In Analytic Geometry

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 5 inches

Select the graph of the equation. r=2−sin⁡(θ−π4)r = 2 - \sin \left( \theta - \frac { \pi } { 4 } \right)r=2−sin(θ−4π​)

Find a set of parametric equations for the rectangular equation. t=2−xt = 2 - xt=2−x y=x2+5y = x ^ { 2 } + 5y=x2+5

Find the equation of the parabola so that its graph matches the description. (y−5)2=2(x+1)( y - 5 ) ^ { 2 } = 2 ( x + 1 )(y−5)2=2(x+1) ; upper half of parabola

Identify the conic as a circle or an ellipse. x2+y2−3x+4y−2=0x ^ { 2 } + y ^ { 2 } - 3 x + 4 y - 2 = 0x2+y2−3x+4y−2=0

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. 9x2+36y2−20x+256y−535=09 x ^ { 2 } + 36 y ^ { 2 } - 20 x + 256 y - 535 = 09x2+36y2−20x+256y−535=0

Find a polar equation of the conic with its focus at the pole. Conics \quad\quad Eccentricity \quad\quad Directrix Ellipse e=65x=−3\quad\quad\quad e = \frac { 6 } { 5 } \quad\quad\quad x = -3e=56​x=−3

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. (3.5,1.62)( 3.5,1.62 )(3.5,1.62)

Select the curve represented by the parametric equations. x=|t-2| y=t+6

Find a set of parametric equations for the rectangular equation. t=2-x y=1-6

Find the vertices and asymptotes of the hyperbola. x249−y2100=1\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 100 } = 149x2​−100y2​=1

Select the graph of degenerate conic. y2−49x2=0y ^ { 2 } - 49 x ^ { 2 } = 0y2−49x2=0

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point (3,−2)( 3 , - 2 )(3,−2)

Find the vertex, focus, and directrix of the parabola. y2=10xy ^ { 2 } = 10 xy2=10x

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Passes through the point (2,4); horizontal axis

Find the standard form of the equation of the ellipse with the given characteristics. Center: (15,5)( 15,5 )(15,5) ; a = 3b; Foci: (5,5),(25,5)( 5,5 ) , ( 25,5 )(5,5),(25,5) , where a - thr semimajor axis, b - semiminor axis.

Select the polar equation with graph.

Find an equation of the ellipse with vertices (±9,0)( \pm 9,0 )(±9,0) and eccentricity e=39e = \frac { 3 } { 9 }e=93​ .

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Select the graph of the equation. $r = 2 - \sin \left( \theta - \frac { \pi } { 4 } \right)$

Find a set of parametric equations for the rectangular equation. $t = 2 - x$ $y = x ^ { 2 } + 5$

Find the equation of the parabola so that its graph matches the description. $( y - 5 ) ^ { 2 } = 2 ( x + 1 )$ ; upper half of parabola

Identify the conic as a circle or an ellipse. $x ^ { 2 } + y ^ { 2 } - 3 x + 4 y - 2 = 0$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $9 x ^ { 2 } + 36 y ^ { 2 } - 20 x + 256 y - 535 = 0$

Find a polar equation of the conic with its focus at the pole. Conics $\quad$ $\quad$ Eccentricity $\quad$ $\quad$ Directrix Ellipse $\quad\quad\quad e = \frac { 6 } { 5 } \quad\quad\quad x = -3$

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $( 3.5,1.62 )$

Find the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 100 } = 1$

Select the graph of degenerate conic. $y ^ { 2 } - 49 x ^ { 2 } = 0$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Horizontal axis and passes through the point $( 3 , - 2 )$

Find the vertex, focus, and directrix of the parabola. $y ^ { 2 } = 10 x$

Find the standard form of the equation of the ellipse with the given characteristics. Center: $( 15,5 )$ ; a = 3b; Foci: $( 5,5 ) , ( 25,5 )$ , where a - thr semimajor axis, b - semiminor axis.

Find an equation of the ellipse with vertices $( \pm 9,0 )$ and eccentricity $e = \frac { 3 } { 9 }$ .