Question

Which is the equation of an ellipse centered at the origin with foci on x-axis, major axis of length 12 and minor axis of length 8?

Answer 1

A

Explanation:

edge

Answer 2

`(x^(2) )/(36)+(y^2)/(16)=1`

Explanation:

Center of the ellipse is at origin (0, 0)

So (h, k) = (0, 0)

Length of major axis = 12

2a = 12

⇒ a = 6

Length of minor axis = 8

⇒ 2b = 8

⇒ b = 4

Since focus is on the x-axis, so it's a horizontal ellipse.

Equation of the horizontal ellipse is in the form of,

`((x-h)^(2) )/(a^2)+((y-k)^2)/(b^2)=1`

By substituting the given values of a, b, and (h, k)

`((x-0)^(2))/(6^2)+((y-0)^2)/(4^2)=1`

`(x^(2) )/(36)+(y^2)/(16)=1`