Question

From the point `A(4,3),` tangent are drawn to the ellipse `(x^2)/(16)+(y^2)/9=1` to touch the ellipse at `B` and `CdotE F` is a tangent to the ellipse parallel to line `B C` and towards point `Adot` Then find the distance of `A` from `E Fdot`

Answer 1

Correct Answer - `|24-4sqrt(18)|//5`
The equation of the chord of contanct is `(x)/(4)+(y)/(3)=1`
`:.` Slop of line `EF=(-3)/(4)`
The equation of line EF is `y=-(3)/(4)x+sqrt(18)`
Therefore, the distance of (4,3) from EF is `|24-4sqrt(18)|//5`