Question : Graph the ellipse and locate the foci. 1) (x^2/36) + (y^2/25) = 1 : 2151868

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Graph the ellipse and locate the foci.

1) (x²/36) + (y²/25) = 1

A) foci at (2√(6), 0) and (-2√(6), 0)

B) foci at (√(11), 0) and (-√(11), 0)

C) foci at (0, √(11)) and (0, -√(11))

 

D) foci at (0, 2√(6)) and (0, -2√(6))

2) (x²/25) + (y²/49) = 1

A) foci at (0, √(39)) and (0, -√(39))

B) foci at (2√(6), 0) and (-2√(6), 0)

C) foci at (√(39), 0) and (-√(39), 0)

D) foci at (0, 2√(6)) and (0, -2√(6))

3) 4x² = 36 - 9y²

A) foci at (2√(3), 0) and (-2√(3), 0)

B) foci at (√(5), 0) and (-√(5), 0)

C) foci at (0, √(5)) and (0, -√(5))

D) foci at (√(13), 0) and (-√(13), 0)

4) 16x² + 4y² = 64

A) foci at (2√(5), 0) and (-2√(5), 0)

B) foci at (√(21), 0) and (-√(21), 0)

C) foci at (0, 2√(3)) and (0, -2√(3))

D) foci at (2√(3), 0) and (-2√(3), 0)

5) (x²/5) + (y²/9) = 1

A) foci at (0, √(5)) and (0, -√(5))

B) foci at (0, 3) and (0, -3)

C) foci at (0, 2) and (0, -2)

D) foci at (2, 0) and (-2, 0)

6) (x²/49) + (y²/45) = 1

A) foci at (2, 0) and (-2, 0)

B) foci at (0, 7) and (0, -7)

C) foci at (0, 2) and (0, -2)

D) foci at (3√(5), 0) and (-3√(5), 0)

7) (x²/(7/2)) + (y²/(9/2)) = 1

Round to the nearest tenth if necessary.

A) foci (1.1, 0) and (0, -1.1)

B) foci (0, 1) and (0, -1)

C) foci (0, 1) and (0, -1)

D) foci (1, 0) and (0, -1)

Find the standard form of the equation of the ellipse and give the location of its foci.

8)

A) (x²/49) + (y²/9) = 1

foci at (-2√(10), 0) and (2√(10), 0)

B) (x²/49) + (y²/9) = 1

foci at (-7, 0) and (7, 0)

C) (x²/49) - (y²/9) = 1

foci at (- 2√(10), 0) and (2√(10), 0)

D) (x²/9) + (y²/49) = 1

foci at (-2√(10), 0) and (2√(10), 0)

9)

A) (x²/49) + (y²/9) = 1

foci at (0, -2√(10)) and (0, 2√(10))

B) (x²/9) + (y²/49) = 1

foci at (0, -7) and (0, 7)

C) (x²/9) + (y²/49) = 1

foci at (0, 7) and (3, 0)

D) (x²/9) + (y²/49) = 1

foci at (0, -2√(10)) and (0, 2√(10))

10)

Center at (-3, 1)

A) ((x + 3)²/9) + ((y - 1)²/36) = 1

foci at (1 + 3√(3), -3) and (1 - 3√(3), -3)

B) ((x - 1)²/36) + ((y + 3)²/9) = 1

foci at (-3 + 3√(3), -3) and (-3 - 3√(3), -3)

C) ((x - 1)²/9) + ((y + 3)²/36) = 1

foci at (- 3√(3), 1) and (3√(3), 1)

D) ((x + 3)²/36) + ((y - 1)²/9) = 1

foci at (-3 + 3√(3), 1) and (-3 - 3√(3), 1)

Find the standard form of the equation of the ellipse satisfying the given conditions.

11) Foci: (-3, 0), (3, 0); vertices: (-8, 0), (8, 0)

A) (x²/9) + (y²/55) = 1

B) (x²/55) + (y²/64) = 1

C) (x²/9) + (y²/64) = 1

D) (x²/64) + (y²/55) = 1

12) Foci: (0, -3), (0, 3); vertices: (0, -8), (0, 8)

A) (x²/64) + (y²/55) = 1

B) (x²/9) + (y²/55) = 1

C) (x²/55) + (y²/64) = 1

D) (x²/9) + (y²/64) = 1

13) Foci: (-3, 0), (3, 0); x-intercepts: -5 and 5

A) (x²/25) + (y²/16) = 1

B) (x²/16) + (y²/25) = 1

C) (x²/9) + (y²/25) = 1

D) (x²/9) + (y²/16) = 1

14) Foci: (0, -4), (0, 4); y-intercepts: -8 and 8

A) (x²/16) + (y²/64) = 1

B) (x²/48) + (y²/64) = 1

C) (x²/16) + (y²/48) = 1

D) (x²/64) + (y²/48) = 1

15) Major axis horizontal with length 12; length of minor axis = 10; center (0, 0)

A) (x²/25) + (y²/36) = 1

B) (x²/12) + (y²/25) = 1

C) (x²/144) + (y²/100) = 1

D) (x²/36) + (y²/25) = 1

16) Major axis vertical with length 18; length of minor axis = 12; center (0, 0)

A) (x²/12) + (y²/81) = 1

B) (x²/144) + (y²/324) = 1

C) (x²/81) + (y²/36) = 1

D) (x²/36) + (y²/81) = 1

17) Endpoints of major axis: (-1, -9) and (-1, 1); endpoints of minor axis: (-3, -4) and (1, -4);

A) ((x + 4)2/4) + ((y + 1)2/25) = 1

B) ((x - 1)2/4) + ((y - 4)2/25) = 1

C) ((x + 1)2/4) + ((y + 4)2/25) = 1

D) ((x - 2)2/4) + ((y - 5)2/25) = 1

18) Endpoints of major axis: (-2, 1) and (10, 1); endpoints of minor axis: (4, -2) and (4, 4)

A) ((x + 4)²/36) + ((y - 3)²/9) = 0

B) ((x + 4)²/36) + ((y - 3)²/9) = 1

C) ((x - 1)²/9) + ((y - 4)²/36) = 1

D) ((x - 4)²/36) + ((y - 1)²/9) = 1