Question

I need this answered From my prep guid, pre calc

Answer 1

Given:

The equation of the ellipse is,

`((x-2)^2)/(36)+((y+3)^2)/(12)=1`

Step-by-step explanation:

The general equation of ellipse with center (h,k) is,

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

The center of te given ellipse is (2,-3).

Determine the value of a and b.

`\begin{gathered} a=\sqrt[]{36} \\ =6 \end{gathered}`
`\begin{gathered} b=\sqrt[]{12} \\ =2\sqrt[]{3} \end{gathered}`

The value of a is more than b. so major axis is horiontal and minor axis is vertical.

The coordinates of endpoints of major axis are,

`(2+6,3)=(8,-3)`

and

`(2-6,3)=(-4,-3)`

The coordinates of endpoints of minor axis,

`(2,-3+2\sqrt[]{3})`

and

`(2,-3-2\sqrt[]{3})`

or we can expressed coordinates of endpoints of minor axis as,

`(2,-3\pm2\sqrt[]{3})`