Question

The ellipse is centered at the origin, its major axis is horizontal, with length 8; the length of its minor axis is 4;

Answer 1

Consider we need to find the equation of ellipse.

Given:

Ellipse is centered at the origin.

Major axis is horizontal, with length 8.

The length of its minor axis is 4.

To find:

The equation of ellipse.

Solution:

Major axis is horizontal, so standard form of ellipse is

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

where, (h,k) is center of the ellipse and length of major axis is 2a and length of minor axis is 2b.

Ellipse is centered at the origin. So, h=0 and k=0.

Major axis is horizontal, with length 8.

`2a=8`

`a=4`

The length of its minor axis is 4.

`2b=4`

`b=2`

Substitute h=0, k=0, a=4 and b=2 in equation (i).

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

`(x^2)/(16)+(y^2)/(4)=1`

Therefore, the required equation of ellipse is
`(x^2)/(16)+(y^2)/(4)=1`.