Question

Find the points on the ellipse `(x^2)/4+(y^2)/9=1` on which the normals are parallel to the line `2x-y=1.`

Answer 1

The normal at `P(2 cos theta,3 sin theta)` is `(2x)/(cos theta)-(3y)/(sin theta)=-5`
Now, this normal is parallel to 2x-y1. Then, `(2//cos theta)/(3//sin theta)=2`
or ` tan theta=(3)/(1)`
`cos theta=+-and sin theta=+-(3)/(sqrt(10))`
Hence, the points are `(2sqrt(10),9sqrt10),(-2//sqrt(10),-9//sqrt(10))`