Quiz about Conic Sections - Hyperbolas

Question 1

Find the center:

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

Accepted Answer

(1,-2)

Answer

(-1,2)

Answer

(-2,1)

Answer

(2,-1)

Question 2

Find the vertices:

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

Accepted Answer

(3,-2) and (-1,-2)

Answer

(1,2) and (-1,2)

Answer

(1, 0) and (1, -4)

Answer

(-1,0) and (-1,4)

Question 3

What are the foci of the graph of $$\frac{\left(y-1\right)^2}{16}-\frac{\left(x+1\right)^2}{4}=1$$

Accepted Answer

$$\left(-1,\ 1\pm2\sqrt{5}\right)$$

Answer

$$\left(1,\ 1\pm2\sqrt{5}\right)$$

Answer

$$\left(1\pm2\sqrt{5},\ 1\right)$$

Answer

$$\left(1,\ 1\pm2\sqrt{5}\right)$$

Question 4

What are the vertices of the hyperbola?

Accepted Answer

(-4, 3) and (-4, -3)

Answer

(0, 3) and (0, -3)

Answer

(0, 1) and (0, -1)

Answer

(4, 0) and (-4, 0)

Question 5

Find the center

Accepted Answer

(-2,1)

Answer

(2,-1)

Answer

(-2,-1)

Answer

(-9,-10)

Question 6

What are the foci of the hyperbola?

Accepted Answer

$$\left(10\pm\sqrt[]{74},-6\right)$$

Answer

$$\left(6\pm\sqrt[]{74},-10\right)$$

Answer

$$\left(10,-6\pm\sqrt[]{74}\right)$$

Answer

$$\left(-10,-6\pm\sqrt[]{74}\right)$$

Question 7

Find the equation of the hyperbola.

Accepted Answer

$$\frac{(x-2)^2}{16}-\frac{(y+3)^2}{20}=1$$

Answer

$$\frac{(x+3)^2}{16}-\frac{(y-2)}{20}=1$$

Answer

$$\frac{(x-2)^2}{20}-\frac{(y+3)^2}{16}=1$$

Answer

$$\frac{(y+3)^2}{16}-\frac{(x-2)^2}{20}=1$$

Conic Sections - Hyperbolas