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