Ellipse Worksheet

**Page 1**

1.

What is the eccentricity of the ellipse 16$x$^{2} + 49$y$^{2} = 784?

a. | 0.43 | ||

b. | 0.82 | ||

c. | 0.22 | ||

d. | - 0.82 |

[Divide throughout by 784.]

This is in the standard form

The focal axis of the ellipse is

[Denominator of

Eccentricity of the ellipse,

[Use the formula.]

=

[Simplify.]

Correct answer : (2)

2.

What is the length of the semi minor axis of the ellipse 64$x$^{2} + 81$y$^{2} = 5184?

a. | 9 | ||

b. | 64 | ||

c. | 81 | ||

d. | 8 |

[Divide both sides by 5184.]

This equation is in the standard form

[Solve for

The focal axis of the ellipse is

[Denominator of

So, the length of the semi minor axis of the ellipse is

Correct answer : (4)

3.

What is the length of the semi major axis of the ellipse 64$x$^{2} + 4$y$^{2} = 256?

a. | 2 | ||

b. | 8 | ||

c. | 64 | ||

d. | 68 |

[Divide both sides by 256.]

This equation is in the standard form

[Solve for

The focal axis of the ellipse is

[Denominator of

So, the length of the semi major axis of the parabola is

Correct answer : (2)

4.

What is the eccentricity of the ellipse 4$x$^{2} + 64$y$^{2} = 256?

a. | 3.87 | ||

b. | 2.06 | ||

c. | 0.97 | ||

d. | 0.12 |

[Divide both sides by 256.]

This is in the standard form

The focal axis of the ellipse is

[Denominator of

Eccentricity of the ellipse =

[Formula.]

=

[Simplify.]

Correct answer : (3)

5.

Find an equation of the ellipse with foci (0, - 4) and (0, 4) whose minor axis has a length of 8 units.

a. | 32$x$ ^{2} + 16$y$^{2} = 1 | ||

b. | $\frac{{y}^{2}}{32}+\frac{{x}^{2}}{16}$ = 1 | ||

c. | $\frac{{x}^{2}}{32}-\frac{{y}^{2}}{16}$ = 1 | ||

d. | $\frac{{x}^{2}}{32}+\frac{{y}^{2}}{16}$ = 1 |

The center of the ellipse is (

[Midpoint of the line segment joining foci.]

Length of the semiminor axis is

[Pythagorean relation.]

So, the standard equation of the ellipse is

Correct answer : (2)

6.

What is the equation of the focal axis of the ellipse $x$^{2} + 9$y$^{2} = 9?

a. | $y$ + $x$ = 0 | ||

b. | $y$ - axis | ||

c. | $y$ = $x$ | ||

d. | $x$ - axis |

[Divide both sides by 9.]

This equation is in the standard form

Correct answer : (4)

7.

What is the equation of the focal axis of the ellipse 64$x$^{2} + $y$^{2} = 64?

a. | $y$ = $x$ | ||

b. | $y$ - axis | ||

c. | $x$ - axis | ||

d. | $y$ + $x$ = 0 |

[Divide both sides by 64.]

This equation is in the standard form

Correct answer : (2)

8.

What are the foci of the ellipse 4$x$^{2} + 64$y$^{2} = 256?

a. | |||

b. | |||

c. | |||

d. |

[Divide both sides by 4.]

This equation is in the standard form

[Pythagorean relation.]

[

The focal axis of the ellipse is

[Denominator of

So, the foci of the ellipse are (±

[Use (±

Correct answer : (4)

9.

What are the foci of the ellipse 9$y$^{2} + 25$x$^{2} = 225?

a. | (± 3, 0) | ||

b. | (0, ± 4) | ||

c. | (0, ± 5) | ||

d. | (± 4, 0) |

[Divide both sides by 225.]

This equation is in the standard form

[Pythagorean relation.]

[

The focal axis of the ellipse is

[Denominator of

So, the foci of the ellipse are (0, ± 4).

[Use (0, ±

Correct answer : (2)

10.

Find the vertices of the ellipse $x$^{2} + 36$y$^{2} = 36.

a. | (0, ± 6) | ||

b. | (± 6, 0) | ||

c. | (± 36, 0) | ||

d. | (0, ± 36) |

[Divide both sides by 36.]

This equation is in the standard form

The focal axis of the ellipse is

[Denominator of

[Solve for

So, the vertices of the ellipse

[Use (±

Correct answer : (2)