Write the standard form of the equation of the ellipse centered at the origin, having a horizontal major axis of 6 units and a minor axis of 4 units.

A) $x26+y24=1\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 4 } = 1$
B) $x29+y24=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$
C) $x216+y236=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 1$
D) $x28+y218=1\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 18 } = 1$
E) $x24+y29=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Question

Write the standard form of the equation of the ellipse centered at the origin, having a horizontal major axis of 6 units and a minor axis of 4 units.

A)

x26+y24=1\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 4 } = 1

B)

x29+y24=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1

C)

x216+y236=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 1

D)

x28+y218=1\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 18 } = 1

E)

x24+y29=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1

Zybrea Knight · Accepted Answer

Final Answer : B, Explanation :   The standard form of the equation of an ellipse centered at the origin with a horizontal major axis is   x 2 a 2 + y 2 b 2 = 1 \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 a 2 x 2 ​ + b 2 y 2 ​ = 1  , where   2 a 2a 2 a   is the length of the major axis and   2 b 2b 2 b   is the length of the minor axis. Given a major axis of 6 units and a minor axis of 4 units,   a = 3 a = 3 a = 3   and   b = 2 b = 2 b = 2  , so the equation becomes   x 2 9 + y 2 4 = 1 \frac{x^2}{9} + \frac{y^2}{4} = 1 9 x 2 ​ + 4 y 2 ​ = 1  .

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