On the ellipse `4x^2+9y^2=1,` the points at which the tangents are parallel to the line `8x=9y` are `(2/5,1/5)` (b) `(-2/5,1/5)` `(-2/5,-1/5)` (d) `(2/5,-1/5)`

Options

A. `(2//5, 1//5)`
B. `(pm 2//5, pm 1//5)`
C. `(-2//5, -1//5)`
D. `(pm2/5, pm 1//5)`

Answer

B

Explanation

We have, `a^(2) = 1/4, b^(2) = 1/9, m = 8/9`
The required points are
`(pm (a^(2)m)/(sqrt(a^(2)m^(2) + b^(2))), pm (b^(2))/(sqrt(a^(2)m^(2) + b^(2)))) = (pm 2/5, pm 1/5)`