Question 1

Find the standard form of the equation of the ellipse with the given characteristics. foci:  endpoints of the major axis: 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the standard form of the equation...

Question 2

Graph the hyperbola. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the hyperbola. 
A) 
B) 
C) 
D)...

Question 3

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0, -1), (10, -1)
Asymptotes: 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the standard form of the equation...

Question 4

Find the equation of the hyperbola with vertices (4, 0), (-4, 0) and focus (7, 0).
A) 
B) 
C) 
D) 
E)none of these0

Accepted Answer

The answer of Find the equation of the hyperbola with...

Question 5

Write the equation of the ellipse with foci at (2, 4), (6, 4), and b = 2.
A) 
B) 
C) 
D) 
E)

Accepted Answer

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

Question 6

Any sound from one focus of an ellipse reflects off the ellipse directly back to the other focus. This property explains whispering galleries such as Statuary Hall in Washington, D.C. The whispering gallery shown in illustration has the shape of a semi-ellipse. Find the distance sound travels as it leaves focus F and returns to focus F'. 
A)59.4 meters
B)29 meters
C)29.7 meters
D)30.3 meters
E)31.4 meters

Accepted Answer

The distance sound travels is equal to the perimeter of the ellipse, which can be approximated using the formula $P = \pi (a+b)$, where $a$ and $b$ are the lengths of the semi-major and semi-minor axes respectively. In this case, we are given that the length of the straight section is 12 meters and the distance between the foci is 20 meters. Since the ellipse is symmetrical, we can assume that the semi-major axis is equal to half of 20 meters which is 10 meters. To find the semi-minor axis, we need to use the fact that the length of the straight section plus twice the semi-minor axis equals 20 meters. Therefore, $12 + 2b = 20$, so $b = 4$. Plugging in these values into the formula gives $P = \pi (10+4) \approx 29.7$ meters. Therefore, the best choice is C.

Question 7

Graph the hyperbola. 
A) 
B) 
C) 
D)

Accepted Answer

The hyperbola has a horizontal axis and a negative coefficient on the x^2 term, which matches the equation of choice B.

Question 8

Identify the conic by writing the equation in standard form. 
A)  ; ellipse
B)  ; ellipse
C)  ; ellipse
D)  ; ellipse
E)  ; circle

Accepted Answer

The standard form equation for an ellipse is:

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$

where (h,k) is the center of the ellipse and a and b are the lengths of the semi-major and semi-minor axes, respectively.

The given equation can be rewritten as:

$-2x^2 + 2y^2 + 880 = 0$

Dividing both sides by 880, we get:

$\frac{-2x^2 + 2y^2}{880} = -1$

Multiplying both sides by -1, we get:

$\frac{2x^2 - 2y^2}{880} = 1$

This is in the standard form equation of an ellipse with center at the origin, semi-major axis of $\sqrt{220}$ and semi-minor axis of $\sqrt{110}$. Thus, the conic is an ellipse and the best choice is (D).

Question 9

Graph the hyperbola. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the hyperbola. 
A) 
B) 
C) 
D)...

Question 10

Write the equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0, 7).
A) 
B) 
C) 
D) 
E)none of these

Accepted Answer

The answer of Write the equation of the ellipse that...

Quiz 10: Topics in Analytic Geometry

Find the standard form of the equation of the ellipse with the given characteristics. foci: endpoints of the major axis:

Graph the hyperbola.

Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (0, -1) , (10, -1) Asymptotes:

Find the equation of the hyperbola with vertices (4, 0) , (-4, 0) and focus (7, 0) .

Write the equation of the ellipse with foci at (2, 4) , (6, 4) , and b = 2.

Graph the hyperbola.

Identify the conic by writing the equation in standard form.

Graph the hyperbola.

Write the equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0, 7) .