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1.

Which of the following is the locus definition of a hyperbola?

a)

The set of all points on a plane equidistant from a fixed point.

b)

The set of all points on a plane equidistant from a fixed point and a fixed line.

c)

The set of all points on a plane whose sum of distances from two fixed points is constant.

d)

The set of all points on a plane whose absolute value of the difference of the distances from two fixed points is constant.

2.

This term pertains to the segment whose endpoints are the vertices of a hyperbola

a)

Transverse Axis

b)

Conjugate Axis

c)

Major Axis

d)

Minor Axis

3.

This term pertains to the segment whose endpoints are the co-vertices of a hyperbola

a)

Transverse Axis

b)

Conjugate Axis

c)

Major Axis

d)

Minor Axis

4.

Given the standard equation of a hyperbola $\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^{2\ }}{b^2}=1$ where $c^2=a^2+b^2$ , What is the length of the transverse axis?

a)

$a$

b)

$2a$

c)

$b$

d)

$2b$

5.

Given the standard equation of a hyperbola $\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^{2\ }}{b^2}=1$ where $c^2=a^2+b^2$ , What is the length of the conjugate axis?

a)

$a$

b)

$2a$

c)

$b$

d)

$2b$

6.

Which of the following are the slopes of the asymptotes of the hyperbola whose equation is $\frac{\left(x-2\right)^2}{36}-\frac{\left(y+1\right)^2}{64}=1$ ?

a)

$\pm\frac{16}{9}$

b)

$\pm\frac{9}{16}$

c)

$\pm\frac{4}{3}$

d)

$\pm\frac{3}{4}$

7.

Which of the following are the slopes of the asymptotes of the hyperbola whose equation is $\frac{\left(y-5\right)^2}{4}-\frac{\left(x+7\right)^2}{9}=1$ ?

a)

$\pm\frac{4}{9}$

b)

$\pm\frac{9}{4}$

c)

$\pm\frac{2}{3}$

d)

$\pm\frac{3}{2}$

8.

What is the orientation of the hyperbola?

\frac{x^2}{4}-\frac{y^2}{25}=1

a)

vertical

b)

horizontal

9.

Determine the length of the transverse axis

a)

1.5

b)

2

c)

3

d)

4

10.

Determine the value of b

a)

1

b)

2

c)

3

d)

4

11.

What is the distance between the 2 foci?

a)

6

b)

8

c)

10

d)

12

12.

Determine the equation of the hyperbola.

a)

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

b)

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

c)

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

d)

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

13.

Determine the equation of the hyperbola.

a)

$\frac{\left(y-1\right)^2}{4}-\frac{\left(x-1\right)^2}{12}=1$

b)

$\frac{y^2}{9}-\frac{x^2}{16}=1$

c)

$\frac{x^2}{16}-\frac{y^2}{9}=1$

d)

$\frac{\left(x-1\right)^2}{16}-\frac{\left(y-1\right)^2}{4}=1$

14.

Which of the following are the coordinates of a vertex of the given hyperbola?

\frac{\left(y-1\right)^2}{4}-\frac{\left(x+2\right)^2}{9}=1

a)

$\left(1,-2\right)$

b)

$\left(-1,2\right)$

c)

$\left(-2,\ -1\right)$

d)

$\left(2,-1\right)$

15.

What is the distance between the two foci of the given hyperbola?

\frac{\left(x+4\right)^2}{36}-\frac{\left(y-5\right)^2}{4}=1

a)

$2\sqrt{10}$

b)

$4\sqrt{10}$

c)

$4\sqrt{2}$

d)

$8\sqrt{2}$

16.

Which is the graph of the hyperbola?

\left(x-1\right)^2-\frac{\left(y+2\right)^2}{9}=1

a)

b)

c)

d)

17.

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

a)

(1, -1)

b)

(-1, 1)

c)

(-1, -1)

d)

(1, 1)

18.

Coordinates of the foci of the hyperbola

\frac{x^2}{9}-\frac{y^2}{16}=1

are

a)

$\left(\pm\ 3,\ 0\right)$

b)

$\left(\pm\ 4,\ 0\right)$

c)

$\left(\pm\ 5,\ 0\right)$

d)

none of these

19.

Which of the following equations is the standard form of the hyperbola whose equation is $9x^2-16y^2-72x-32y-16=0$ ?

a)

$\frac{\left(x-4\right)^2}{16}-\frac{\left(y+1\right)^2}{9}=1$

b)

$\frac{\left(x-4\right)^2}{\frac{16}{9}}-\frac{\left(y+1\right)^2}{16}=1$

c)

$\frac{\left(x-4\right)^2}{\frac{9}{176}}-\frac{\left(y+1\right)^2}{11}=1$

d)

$\frac{\left(x-4\right)^2}{\frac{11}{3}}-\frac{\left(y+1\right)^2}{\frac{33}{16}}=1$

20.

Which of the following are the coordinates of the center of the hyperbola whose equation is $9x^2-16y^2-72x-32y-16=0$ ?

a)

$\left(-1,4\right)$

b)

$\left(1,-4\right)$

c)

$\left(4,-1\right)$

d)

$\left(-4,1\right)$

21.

Which of the following are the coordinates of the vertices of the hyperbola whose equation is $9x^2-16y^2-72x-32y-16=0$ ?

a)

$\left(4,2\right)\ and\ \left(4,-4\right)$

b)

$\left(-1,-1\right)\ and\ \left(9,-1\right)$

c)

$\left(4,3\right)\ and\ \left(4,-5\right)$

d)

$\left(0,-1\right)\ and\ \left(8,-1\right)$

22.

Which of the following are the coordinates of the co-vertices of the hyperbola whose equation is $9x^2-16y^2-72x-32y-16=0$ ?

a)

$\left(4,2\right)\ and\ \left(4,-4\right)$

b)

$\left(-1,-1\right)\ and\ \left(9,-1\right)$

c)

$\left(4,4\right)\ and\ \left(4,-6\right)$

d)

$\left(0,-1\right)\ and\ \left(8,-1\right)$

23.

Which of the following are the coordinates of the foci of the hyperbola whose equation is $9x^2-16y^2-72x-32y-16=0$ ?

a)

$\left(4,2\right)\ and\ \left(4,-4\right)$

b)

$\left(-1,-1\right)\ and\ \left(9,-1\right)$

c)

$\left(4,4\right)\ and\ \left(4,-6\right)$

d)

$\left(0,-1\right)\ and\ \left(8,-1\right)$

24.

Which of the following are the equations of the asymptotes of the hyperbola whose equation is $9x^2-16y^2-72x-32y-16=0$ ?

a)

$y+1=\pm\frac{3}{4}\left(x-4\right)$

b)

$y-4=\pm\frac{3}{4}\left(x+1\right)$

c)

$y+1=\pm\frac{4}{3}\left(x-4\right)$

d)

$y-4=\pm\frac{4}{3}\left(x+1\right)$

25.

Which of the following equations is the standard form of the hyperbola whose equation is $16y^2-9x^2+96y+18x-441=0$ ?

a)

$\frac{\left(x-1\right)^2}{36}-\frac{\left(y+3\right)^2}{64}=1$

b)

$\frac{\left(x-1\right)^2}{64}-\frac{\left(y+3\right)^2}{36}=1$

c)

$\frac{\left(y-3\right)^2}{36}-\frac{\left(x+1\right)^2}{64}=1$

d)

$\frac{\left(y+3\right)^2}{36}-\frac{\left(x-1\right)^2}{64}=1$

26.

Which of the following are the coordinates of the center of the hyperbola whose equation is $16y^2-9x^2+96y+18x-441=0$ ?

a)

$\left(-3,1\right)$

b)

$\left(3,-1\right)$

c)

$\left(-1,3\right)$

d)

$\left(1,-3\right)$

27.

Which of the following are the coordinates of the vertices of the hyperbola whose equation is $16y^2-9x^2+96y+18x-441=0$ ?

a)

$\left(7,-3\right)\ and\ \left(-5,-3\right)$

b)

$\left(1,-9\right)\ and\ \left(1,3\right)$

c)

$\left(11,-9\right)\ and\ \left(-9,-9\right)$

d)

$\left(-7,-3\right)\ and\ \left(9,-3\right)$

28.

Which of the following are the coordinates of the co-vertices of the hyperbola whose equation is $16y^2-9x^2+96y+18x-441=0$ ?

a)

$\left(1,5\right)\ and\ \left(1,-11\right)$

b)

$\left(1,-9\right)\ and\ \left(1,3\right)$

c)

$\left(11,-9\right)\ and\ \left(-9,-9\right)$

d)

$\left(-7,-3\right)\ and\ \left(9,-3\right)$

29.

Which of the following are the coordinates of the foci of the hyperbola whose equation is $16y^2-9x^2+96y+18x-441=0$ ?

a)

$\left(1,7\right)\ and\ \left(1,-13\right)$

b)

$\left(1,-9\right)\ and\ \left(1,3\right)$

c)

$\left(11,-9\right)\ and\ \left(-9,-9\right)$

d)

$\left(-7,-3\right)\ and\ \left(9,-3\right)$

30.

Which of the following are the equations of the asymptotes of the hyperbola whose equation is $16y^2-9x^2+96y+18x-441=0$ ?

a)

$y+3=\pm\frac{4}{3}\left(x-1\right)$

b)

$y+3=\pm\frac{3}{4}\left(x-1\right)$

c)

$y-1=\pm\frac{4}{3}\left(x+3\right)$

d)

$y-1=\pm\frac{3}{4}\left(x+3\right)$

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Total questions: 30

Worksheet time: 1hrs 17mins

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