Find any points of intersection of the graphs algebraically. $\begin{array} { l } - x ^ { 2 } + y ^ { 2 } + 2 x - 7 y + 6 = 0 \\ x ^ { 2 } + y ^ { 2 } - 2 x - 7 y + 6 = 0 \end{array}$

A) The points of intersection are $( 2,2 )$ and $( 3,3 )$ . B) The points of intersection are $( - 2 , - 2 )$ and $( 2,3 )$ . C) The points of intersection are $( 3,3 )$ and $( 3,3 )$ . D) The points of intersection are $( 2,2 )$ and $( 2,3 )$ . E) The points of intersection are $( 3,3 )$ and $( - 3 , - 3 )$ . A) The points of intersection are $( 2,2 )$ and $( 3,3 )$ . B) The points of intersection are $( - 2 , - 2 )$ and $( 2,3 )$ . C) The points of intersection are $( 3,3 )$ and $( 3,3 )$ . D) The points of intersection are $( 2,2 )$ and $( 2,3 )$ . E) The points of intersection are $( 3,3 )$ and $( - 3 , - 3 )$ .

Exam 10: Topics In Analytic Geometry

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $3 x - 6 y - 11 = 0$

(Multiple Choice)

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Question 421

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line.

(Multiple Choice)

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Question 422

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. Earth $a = 95.956 \times 10 ^ { 6 }$ miles $e = 0.0167$

(Multiple Choice)

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Question 423

Use the discriminant to classify the graph. $100 x ^ { 2 } - 100 x y + 25 y ^ { 2 } + 12 y = 0$

(Multiple Choice)

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Question 424

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } - 6 x - 3 y + 8 = 0$

(Multiple Choice)

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Question 425

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4) focies: (0,±5)

(Multiple Choice)

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Question 426

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = 3

(Multiple Choice)

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Question 427

Find any points of intersection of the graphs algebraically. -++2x-7y+6=0 +-2x-7y+6=0

(Multiple Choice)

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Question 428

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$

(Multiple Choice)

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Question 429

Find the center and radius of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$

(Multiple Choice)

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Question 430

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = \sqrt { t }$ $y = 4 - t$

(Multiple Choice)

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Question 431

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse. $\frac { x ^ { 2 } } { 4 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 49 } = 1$

(Multiple Choice)

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Question 432

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 5

(Multiple Choice)

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Question 433

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

(Multiple Choice)

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Question 434

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( 0 , \pm 14 )$ ; asymptotes: $y = \pm 7 x$

(Multiple Choice)

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Question 435

Select the parametric equations matching with the following graph.

(Multiple Choice)

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Question 436

Identify the conic and select its correct graph. $r = \frac { 8 } { 2 - \cos \theta }$

(Multiple Choice)

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Question 437

As a speeding train crosses a trestle over a deep gorge, a child drops his toy plane from the window.The path of the toy plane is modeled by $x ^ { 2 } = - 7.0 ( y - 185 )$ , where y is the height above the floor of the gorge and distances are measured in feet.How far will the toy plane travel horizontally before it hits the bottom of the gorge? [Note: The toy plane does not glide; it "drops like a rock."]

(Multiple Choice)

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Question 438

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 2,2 )$

(Multiple Choice)

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Question 439

Give the coordinates of the circle's center and its radius. $( x - 6 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4$

(Multiple Choice)

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Question 440

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $3 x - 6 y - 11 = 0$

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line.

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. Earth $a = 95.956 \times 10 ^ { 6 }$ miles $e = 0.0167$

Use the discriminant to classify the graph. $100 x ^ { 2 } - 100 x y + 25 y ^ { 2 } + 12 y = 0$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } - 6 x - 3 y + 8 = 0$

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4) focies: (0,±5)

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = 3

Find any points of intersection of the graphs algebraically. -++2x-7y+6=0 +-2x-7y+6=0

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$

Find the center and radius of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = \sqrt { t }$ $y = 4 - t$

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse. $\frac { x ^ { 2 } } { 4 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 49 } = 1$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 5

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( 0 , \pm 14 )$ ; asymptotes: $y = \pm 7 x$

Select the parametric equations matching with the following graph.

Identify the conic and select its correct graph. $r = \frac { 8 } { 2 - \cos \theta }$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 2,2 )$

Give the coordinates of the circle's center and its radius. $( x - 6 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4$

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

Find the inclination θ\thetaθ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. 3x−6y−11=03 x - 6 y - 11 = 03x−6y−11=0

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line. ​

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. Earth a=95.956×106a = 95.956 \times 10 ^ { 6 }a=95.956×106 miles e=0.0167e = 0.0167e=0.0167

Use the discriminant to classify the graph. 100x2−100xy+25y2+12y=0100 x ^ { 2 } - 100 x y + 25 y ^ { 2 } + 12 y = 0100x2−100xy+25y2+12y=0

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. x2−6x−3y+8=0x ^ { 2 } - 6 x - 3 y + 8 = 0x2−6x−3y+8=0

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0,±4) focies: (0,±5)

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Directrix: x = 3

Find any points of intersection of the graphs algebraically. -++2x-7y+6=0 +-2x-7y+6=0

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: (−72,0)\left( - \frac { 7 } { 2 } , 0 \right)(−27​,0)

Find the center and radius of the conic. x264+y264=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 164x2​+64y2​=1

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=tx = \sqrt { t }x=t​ y=4−ty = 4 - ty=4−t

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse. x24/49+(y+1)24/49=1\frac { x ^ { 2 } } { 4 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 49 } = 14/49x2​+4/49(y+1)2​=1

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 5

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: (0,±14)( 0 , \pm 14 )(0,±14) ; asymptotes: y=±7xy = \pm 7 xy=±7x

Select the parametric equations matching with the following graph.

Identify the conic and select its correct graph. r=82−cos⁡θr = \frac { 8 } { 2 - \cos \theta }r=2−cosθ8​

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. (2,2)( 2,2 )(2,2)

Give the coordinates of the circle's center and its radius. (x−6)2+(y+5)2=4( x - 6 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4(x−6)2+(y+5)2=4

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

Find the inclination $\theta$ (in radians and degrees) of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $3 x - 6 y - 11 = 0$

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line.

Find the polar equation of the planet's orbit and the perihelion and aphelion distances. Earth $a = 95.956 \times 10 ^ { 6 }$ miles $e = 0.0167$

Use the discriminant to classify the graph. $100 x ^ { 2 } - 100 x y + 25 y ^ { 2 } + 12 y = 0$

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $x ^ { 2 } - 6 x - 3 y + 8 = 0$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$

Find the center and radius of the conic. $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 64 } = 1$

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $x = \sqrt { t }$ $y = 4 - t$

Identify the conic as a circle or an ellipse then find the radius for circle or center for ellipse. $\frac { x ^ { 2 } } { 4 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 49 } = 1$

Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin. Vertices: $( 0 , \pm 14 )$ ; asymptotes: $y = \pm 7 x$

Identify the conic and select its correct graph. $r = \frac { 8 } { 2 - \cos \theta }$

A point in rectangular coordinates is given.Convert the point to polar coordinates, r > 0. $( 2,2 )$

Give the coordinates of the circle's center and its radius. $( x - 6 ) ^ { 2 } + ( y + 5 ) ^ { 2 } = 4$