Question 1

In three-dimensional space, what is the equation of the set of points that are 12 units from the point  (1,5,-4)  ?

Accepted Answer

The answer of In three-dimensional space, what is the equation...

Question 2

The point  (-5,-4,8)  is what distance from the  y z -plane?

Accepted Answer

A)   -5 
B)   -4 
C)  4 
D)  5 
E)  8 
A)   -5 
B)   -4 
C)  4 
D)  5 
E)  8

Question 3

Find the equation for the conic in standard form. Identify the conic.
$x=5+2 \cos t, y=-2+\sin t, 0 \leq t \leq 2 \pi$

Accepted Answer

The answer of Find the equation for the conic in...

Question 4

What is the equation of the parabola with vertex  (-4,-4)  that passes through  (0,0)  and has its axis of symmetry parallel to the  x -axis?

Accepted Answer

The answer of What is the equation of the parabola...

Question 5

For the hyperbola $\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1$
find the center, foci, endpoints of the transverse axis, and the equations of the asymptotes.

Accepted Answer

Center: @#LAT-DLM&
Foci: @#LAT-DLM&;
End

Question 6

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

Accepted Answer

x=4+5t, y

Question 7

Identify the type of conic given by the equation $2 x^{2}-x y+3 y^{2}-x-4 y-6=0$

Accepted Answer

The answer of Identify the type of conic given by...

Question 8

Find an equation in standard form for the hyperbola centered at  (1,-4) , with one focus at  (7,-4)  and eccentricity  e=2 .

Accepted Answer

The answer of Find an equation in standard form for...

Question 9

Use the discriminant $B^{2}-4 A C$ to determine if $3 x^{2}-12 x y+4 y^{2}+x-5 y-4=0$  is an ellipse, a parabola, or a hyperbola.

Accepted Answer

The answer of Use the discriminant $B^{2}-4 A C$ to...

Question 10

What is the magnitude of the vector $\mathbf{v}=\langle 2,-1,3\rangle ?$

Accepted Answer

The answer of What is the magnitude of the vector...

Question 11

Which of the following are the vertices of the hyperbola $\frac{(x-3)^{2}}{25}-\frac{(y+5)^{2}}{169}=1 ?$

Accepted Answer

A)   (3,8)  and  (3,-18) 
B)   (8,-5)  and  (-2,-5) 
C)   (3,8)  and  (3,-13) 
D)   (16,-5)  and  (-10,-5) 
A)   (3,8)  and  (3,-18) 
B)   (8,-5)  and  (-2,-5) 
C)   (3,8)  and  (3,-13) 
D)   (16,-5)  and  (-10,-5)

Question 12

$\text { Sketch the graph of the hyperbola  }  .$ $\frac{(y-5)^{2}}{9}-\frac{(x-3)^{2}}{25}=1$

Accepted Answer

The answer of \(\text { Sketch the graph of the...

Question 13

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 14

Find an equation in standard form for the ellipse whose major axis endpoints are  (-5,2)  and  (3,2)  and whose minor axis has length 6 .

Accepted Answer

The answer of Find an equation in standard form for...

Question 15

Write the equation of the conic with focus  (2,-3)  and directrix  y=5 .

Accepted Answer

The answer of Write the equation of the conic with...

Question 16

Sketch the graph of the hyperbola $\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1$.

Accepted Answer

The answer of Sketch the graph of the hyperbola $\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1$....

Question 17

Find the equation for the conic in standard form. Identify the conic. $x=2+2 \cos t, y=-2+2 \sin t, 0 \leq t \leq 2 \pi$

Accepted Answer

The answer of Find the equation for the conic in...

Question 18

Determine the directrix of the conic with polar form $r=6 /(3-\cos \theta)$

Accepted Answer

The answer of Determine the directrix of the conic with...

Question 19

Sketch a graph of the equation $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$

Accepted Answer

The answer of Sketch a graph of the equation $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$...

Question 20

For the equation  $2 x^{2}-x y-3 y^{2}-2 x+4 y-6=0$, 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...

In three-dimensional space, what is the equation of the set of points that are 12 units from the point (1,5,-4) ?

The point (-5,-4,8) is what distance from the y z -plane?

Find the equation for the conic in standard form. Identify the conic. $x=5+2 \cos t, y=-2+\sin t, 0 \leq t \leq 2 \pi$

What is the equation of the parabola with vertex (-4,-4) that passes through (0,0) and has its axis of symmetry parallel to the x -axis?

For the hyperbola $\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1$ find the center, foci, endpoints of the transverse axis, and the equations of the asymptotes.

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

Identify the type of conic given by the equation $2 x^{2}-x y+3 y^{2}-x-4 y-6=0$

Find an equation in standard form for the hyperbola centered at (1,-4) , with one focus at (7,-4) and eccentricity e=2 .

Use the discriminant $B^{2}-4 A C$ to determine if $3 x^{2}-12 x y+4 y^{2}+x-5 y-4=0$ is an ellipse, a parabola, or a hyperbola.

What is the magnitude of the vector $\mathbf{v}=\langle 2,-1,3\rangle ?$

Which of the following are the vertices of the hyperbola $\frac{(x-3)^{2}}{25}-\frac{(y+5)^{2}}{169}=1 ?$

$\text { Sketch the graph of the hyperbola } .$ $\frac{(y-5)^{2}}{9}-\frac{(x-3)^{2}}{25}=1$ $\text { Sketch the graph of the hyperbola } . \frac{(y-5)^{2}}{9}-\frac{(x-3)^{2}}{25}=1$

Find an equation in standard form for the ellipse whose major axis endpoints are (-5,2) and (3,2) and whose minor axis has length 6 .

Write the equation of the conic with focus (2,-3) and directrix y=5 .

Sketch the graph of the hyperbola $\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1$ . $Sketch the graph of the hyperbola \frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1 .$

Find the equation for the conic in standard form. Identify the conic. $x=2+2 \cos t, y=-2+2 \sin t, 0 \leq t \leq 2 \pi$

Determine the directrix of the conic with polar form $r=6 /(3-\cos \theta)$

Sketch a graph of the equation $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$

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

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

Exam 8: Analytic Geometry in Two and Three Dimensions

In three-dimensional space, what is the equation of the set of points that are 12 units from the point (1,5,-4) ?

The point (-5,-4,8) is what distance from the y z -plane?

Find the equation for the conic in standard form. Identify the conic. x=5+2cos⁡t,y=−2+sin⁡t,0≤t≤2πx=5+2 \cos t, y=-2+\sin t, 0 \leq t \leq 2 \pix=5+2cost,y=−2+sint,0≤t≤2π

What is the equation of the parabola with vertex (-4,-4) that passes through (0,0) and has its axis of symmetry parallel to the x -axis?

For the hyperbola (x+2)24−(y−5)216=1\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=14(x+2)2​−16(y−5)2​=1 find the center, foci, endpoints of the transverse axis, and the equations of the asymptotes.

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

Identify the type of conic given by 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

Find an equation in standard form for the hyperbola centered at (1,-4) , with one focus at (7,-4) and eccentricity e=2 .

Use the discriminant B2−4ACB^{2}-4 A CB2−4AC to determine if 3x2−12xy+4y2+x−5y−4=03 x^{2}-12 x y+4 y^{2}+x-5 y-4=03x2−12xy+4y2+x−5y−4=0 is an ellipse, a parabola, or a hyperbola.

What is the magnitude of the vector v=⟨2,−1,3⟩?\mathbf{v}=\langle 2,-1,3\rangle ?v=⟨2,−1,3⟩?

Which of the following are the vertices of the hyperbola (x−3)225−(y+5)2169=1?\frac{(x-3)^{2}}{25}-\frac{(y+5)^{2}}{169}=1 ?25(x−3)2​−169(y+5)2​=1?

Sketch the graph of the hyperbola .\text { Sketch the graph of the hyperbola } . Sketch the graph of the hyperbola . (y−5)29−(x−3)225=1\frac{(y-5)^{2}}{9}-\frac{(x-3)^{2}}{25}=19(y−5)2​−25(x−3)2​=1

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​?

Find an equation in standard form for the ellipse whose major axis endpoints are (-5,2) and (3,2) and whose minor axis has length 6 .

Write the equation of the conic with focus (2,-3) and directrix y=5 .

Sketch the graph of the hyperbola (x+2)24−(y−5)216=1\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=14(x+2)2​−16(y−5)2​=1 .

Find the equation for the conic in standard form. Identify the conic. x=2+2cos⁡t,y=−2+2sin⁡t,0≤t≤2πx=2+2 \cos t, y=-2+2 \sin t, 0 \leq t \leq 2 \pix=2+2cost,y=−2+2sint,0≤t≤2π

Determine the directrix of the conic with polar form r=6/(3−cos⁡θ)r=6 /(3-\cos \theta)r=6/(3−cosθ)

Sketch a graph of the equation x29+y216=1\frac{x^{2}}{9}+\frac{y^{2}}{16}=19x2​+16y2​=1

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

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

Find the equation for the conic in standard form. Identify the conic. $x=5+2 \cos t, y=-2+\sin t, 0 \leq t \leq 2 \pi$

For the hyperbola $\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1$ find the center, foci, endpoints of the transverse axis, and the equations of the asymptotes.

Identify the type of conic given by the equation $2 x^{2}-x y+3 y^{2}-x-4 y-6=0$

Use the discriminant $B^{2}-4 A C$ to determine if $3 x^{2}-12 x y+4 y^{2}+x-5 y-4=0$ is an ellipse, a parabola, or a hyperbola.

What is the magnitude of the vector $\mathbf{v}=\langle 2,-1,3\rangle ?$

Which of the following are the vertices of the hyperbola $\frac{(x-3)^{2}}{25}-\frac{(y+5)^{2}}{169}=1 ?$

$\text { Sketch the graph of the hyperbola } .$ $\frac{(y-5)^{2}}{9}-\frac{(x-3)^{2}}{25}=1$ $\text { Sketch the graph of the hyperbola } . \frac{(y-5)^{2}}{9}-\frac{(x-3)^{2}}{25}=1$

Sketch the graph of the hyperbola $\frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1$ . $Sketch the graph of the hyperbola \frac{(x+2)^{2}}{4}-\frac{(y-5)^{2}}{16}=1 .$

Find the equation for the conic in standard form. Identify the conic. $x=2+2 \cos t, y=-2+2 \sin t, 0 \leq t \leq 2 \pi$

Determine the directrix of the conic with polar form $r=6 /(3-\cos \theta)$

Sketch a graph of the equation $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$

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