Question

Find an equation of the ellipse that has center (-2,4), a minor axis of length 12, and a vertex at (5, 4).

Answer 1

Given:

The centre of the ellipse = (-2,4),

A minor axis length a= 12 ,

And distence from the vertex(5,4) to centre ,

`\begin{gathered} b=\sqrt[]{(5-(-2))^2+(4-4)^2} \\ =\sqrt[]{(5+2)^2+0} \\ =\sqrt[]{7^2} \\ =7 \end{gathered}`

The equation of ellipse is ,

`\begin{gathered} ((x-(-2))^2)/(7^2)+((y-4)^2)/(12^2)=1 \\ ((x+2)^2)/(49)+((y-4)^2)/(144)=1 \\ \end{gathered}`