Question 1

What is the equation of the parabola with vertex  (-2,-2)  that passes through  (0,0)  and has its axis of symmetry parallel to the  x -axis?

Accepted Answer

$y=\frac{1}{2}(x+2)^{2}-2$

Question 2

Write the equation of the conic with focus  (3,4)  and directrix  x=1 .

Accepted Answer

$x=\frac{1}{4}(y-4)^{2}+2$

Question 3

What is the vertex of the parabola 
$5 x^{2}-40 x-y+78=0 ?$

Accepted Answer

(4,-2)

Question 4

A telecommunications satellite is a paraboloid of revolution with a diameter of  8 ft and depth of  3 ft. How far from the vertex should the receiving antenna be placed?

Accepted Answer

The antenna should b

Question 5

Write the parametric equations for the line through the points  (-1,2,4)  and  (6,0,-3) .

Accepted Answer

x=-1+7 t,

Question 6

Find the vertex of the parabola $y=4 x^{2}+8 x-6$

Accepted Answer

The answer of Find the vertex of the parabola \(y=4...

Question 7

For the equation $2 x^{2}-x y+3 y^{2}-x-4 y-6=0$, solve for  y  to obtain equation(s) that could be entered into your grapher.

Accepted Answer

The answer of For the equation \(2 x^{2}-x y+3 y^{2}-x-4...

Question 8

After translation of coordinate axes, a quadratic
equation becomes $\frac{\left(x^{\prime}\right)^{2}}{16}+\frac{\left(y^{\prime}\right)^{2}}{9}=1$
had the effect of moving the point  (x, y)=(1,-2)  to
the point $\left(x^{\prime}, y^{\prime}\right)=(0,0)$
equation in  x y  coordinates?

Accepted Answer

A)  $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ 
B)  $\frac{(x+1)^{2}}{16}+\frac{(y-2)^{2}}{9}=1$ 
C)  $\frac{(x-1)^{2}}{16}+\frac{(y+2)^{2}}{9}=1$ 
D)  $\frac{\left(x^{\prime}-1\right)^{2}}{16}+\frac{\left(y^{\prime}+2\right)^{2}}{9}=1$ 
A)  $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ 
B)  $\frac{(x+1)^{2}}{16}+\frac{(y-2)^{2}}{9}=1$ 
C)  $\frac{(x-1)^{2}}{16}+\frac{(y+2)^{2}}{9}=1$ 
D)  $\frac{\left(x^{\prime}-1\right)^{2}}{16}+\frac{\left(y^{\prime}+2\right)^{2}}{9}=1$

Question 9

For the points  A(-2,4,6), B(0,6,-2)  and  C(4,-8,6) , what is the distance from point  A  to the midpoint of line segment  BC?

Accepted Answer

The answer of For the points  A(-2,4,6), B(0,6,-2) ...

Question 10

$\text { Draw the graph of } r=4 /(2+\cos \theta)$

Accepted Answer

The answer of \(\text { Draw the graph of }...

Question 11

Which of the following is the graph of the plane  2 x+6 y+z=1  ?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

In three-dimensional space, what are the parametric equations for the line through the points  (2,-1,3)  and  (-1,4,0)?

Accepted Answer

x=2+3t ;

Question 13

A telecommunications satellite is a paraboloid of revolution with a diameter of  6 ft and depth of  3 ft. How far from the vertex should the receiving antenna be placed?

Accepted Answer

The antenna should b

Question 14

Find a polar equation for an ellipse with a focus at  (0,0)  if the endpoints of its major axis have polar coordinates $(5, \pi) \text { and }(3,2 \pi)$

Accepted Answer

The answer of Find a polar equation for an ellipse...

Question 15

Find a polar equation for an ellipse with a focus at  (0,0)  if the endpoints of its major axis have polar coordinates $(5, \pi / 2)$ and $(3,3 \pi / 2)$

Accepted Answer

The answer of Find a polar equation for an ellipse...

Question 16

What is the equation, in standard form, of the parabola with focus  (3,0)  and directrix  x=-3  ?

Accepted Answer

The answer of What is the equation, in standard form,...

Question 17

Find a polar equation for the conic with focus at  (0,0) , eccentricity  4 / 3 , and directrix  y=7 .

Accepted Answer

The answer of Find a polar equation for the conic...

Question 18

The point  (-3,-2,10)  is what distance from the  xz -plane?

Accepted Answer

A)   -3 
B)   -2 
C)  2 
D)  3 
E)  10 
A)   -3 
B)   -2 
C)  2 
D)  3 
E)  10

Question 19

In a whispering gallery, any sound at one focus of an ellipse reflects off the ellipse directly to the other focus. The figure shows an elliptical whispering gallery, where  x  is the center of the ellipse. What is the distance that sound travels from focus $F_{1}$ to focus $F_{2} ?$

Accepted Answer

The answer of In a whispering gallery, any sound at...

Question 20

Identify the conic $r=\frac{24}{5+8 \cos \theta}$ without drawing its graph. State the eccentricity and directrix.

Accepted Answer

Hyperbola:

What is the equation of the parabola with vertex (-2,-2) that passes through (0,0) and has its axis of symmetry parallel to the x -axis?

Write the equation of the conic with focus (3,4) and directrix x=1 .

What is the vertex of the parabola $5 x^{2}-40 x-y+78=0 ?$

A telecommunications satellite is a paraboloid of revolution with a diameter of 8 ft and depth of 3 ft. How far from the vertex should the receiving antenna be placed?

Write the parametric equations for the line through the points (-1,2,4) and (6,0,-3) .

Find the vertex of the parabola $y=4 x^{2}+8 x-6$

For the equation $2 x^{2}-x y+3 y^{2}-x-4 y-6=0$ , solve for y to obtain equation(s) that could be entered into your grapher.

After translation of coordinate axes, a quadratic equation becomes $\frac{\left(x^{\prime}\right)^{2}}{16}+\frac{\left(y^{\prime}\right)^{2}}{9}=1$ had the effect of moving the point (x, y)=(1,-2) to the point $\left(x^{\prime}, y^{\prime}\right)=(0,0)$ equation in x y coordinates?

For the points A(-2,4,6), B(0,6,-2) and C(4,-8,6) , what is the distance from point A to the midpoint of line segment BC?

$\text { Draw the graph of } r=4 /(2+\cos \theta)$ $\text { Draw the graph of } r=4 /(2+\cos \theta)$

Which of the following is the graph of the plane 2 x+6 y+z=1 ?

In three-dimensional space, what are the parametric equations for the line through the points (2,-1,3) and (-1,4,0)?

A telecommunications satellite is a paraboloid of revolution with a diameter of 6 ft and depth of 3 ft. How far from the vertex should the receiving antenna be placed?

Find a polar equation for an ellipse with a focus at (0,0) if the endpoints of its major axis have polar coordinates $(5, \pi) \text { and }(3,2 \pi)$

Find a polar equation for an ellipse with a focus at (0,0) if the endpoints of its major axis have polar coordinates $(5, \pi / 2)$ and $(3,3 \pi / 2)$

What is the equation, in standard form, of the parabola with focus (3,0) and directrix x=-3 ?

Find a polar equation for the conic with focus at (0,0) , eccentricity 4 / 3 , and directrix y=7 .

The point (-3,-2,10) is what distance from the xz -plane?

Identify the conic $r=\frac{24}{5+8 \cos \theta}$ without drawing its graph. State the eccentricity and directrix.

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Discrete Mathematics

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

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Exam 8: Analytic Geometry in Two and Three Dimensions

What is the equation of the parabola with vertex (-2,-2) that passes through (0,0) and has its axis of symmetry parallel to the x -axis?

Write the equation of the conic with focus (3,4) and directrix x=1 .

What is the vertex of the parabola 5x2−40x−y+78=0?5 x^{2}-40 x-y+78=0 ?5x2−40x−y+78=0?

A telecommunications satellite is a paraboloid of revolution with a diameter of 8 ft and depth of 3 ft. How far from the vertex should the receiving antenna be placed?

Write the parametric equations for the line through the points (-1,2,4) and (6,0,-3) .

Find the vertex of the parabola y=4x2+8x−6y=4 x^{2}+8 x-6y=4x2+8x−6

For the equation 2x2−xy+3y2−x−4y−6=02 x^{2}-x y+3 y^{2}-x-4 y-6=02x2−xy+3y2−x−4y−6=0 , solve for y to obtain equation(s) that could be entered into your grapher.

For the points A(-2,4,6), B(0,6,-2) and C(4,-8,6) , what is the distance from point A to the midpoint of line segment BC?

Draw the graph of r=4/(2+cos⁡θ)\text { Draw the graph of } r=4 /(2+\cos \theta) Draw the graph of r=4/(2+cosθ)

Which of the following is the graph of the plane 2 x+6 y+z=1 ?

In three-dimensional space, what are the parametric equations for the line through the points (2,-1,3) and (-1,4,0)?

A telecommunications satellite is a paraboloid of revolution with a diameter of 6 ft and depth of 3 ft. How far from the vertex should the receiving antenna be placed?

Find a polar equation for an ellipse with a focus at (0,0) if the endpoints of its major axis have polar coordinates (5,π) and (3,2π)(5, \pi) \text { and }(3,2 \pi)(5,π) and (3,2π)

Find a polar equation for an ellipse with a focus at (0,0) if the endpoints of its major axis have polar coordinates (5,π/2)(5, \pi / 2)(5,π/2) and (3,3π/2)(3,3 \pi / 2)(3,3π/2)

What is the equation, in standard form, of the parabola with focus (3,0) and directrix x=-3 ?

Find a polar equation for the conic with focus at (0,0) , eccentricity 4 / 3 , and directrix y=7 .

The point (-3,-2,10) is what distance from the xz -plane?

In a whispering gallery, any sound at one focus of an ellipse reflects off the ellipse directly to the other focus. The figure shows an elliptical whispering gallery, where x is the center of the ellipse. What is the distance that sound travels from focus F1F_{1}F1​ to focus F2?F_{2} ?F2​?

Identify the conic r=245+8cos⁡θr=\frac{24}{5+8 \cos \theta}r=5+8cosθ24​ without drawing its graph. State the eccentricity and directrix.

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Discrete Mathematics

An Introduction to Calculus: Limits, Derivatives, and Integrals

P Prerequisites

Mathematical Problem Set

Filters

What is the vertex of the parabola $5 x^{2}-40 x-y+78=0 ?$

Find the vertex of the parabola $y=4 x^{2}+8 x-6$

For the equation $2 x^{2}-x y+3 y^{2}-x-4 y-6=0$ , solve for y to obtain equation(s) that could be entered into your grapher.

$\text { Draw the graph of } r=4 /(2+\cos \theta)$ $\text { Draw the graph of } r=4 /(2+\cos \theta)$

Find a polar equation for an ellipse with a focus at (0,0) if the endpoints of its major axis have polar coordinates $(5, \pi) \text { and }(3,2 \pi)$

Find a polar equation for an ellipse with a focus at (0,0) if the endpoints of its major axis have polar coordinates $(5, \pi / 2)$ and $(3,3 \pi / 2)$

Identify the conic $r=\frac{24}{5+8 \cos \theta}$ without drawing its graph. State the eccentricity and directrix.