JEE Advance - Mathematics (1999 - No. 33)
On the ellipse $$4{x^2} + 9{y^2} = 1,$$ the points at which the tangents are parallel to the line $$8x = 9y$$ are
$$\left( {{2 \over 5},{1 \over 5}} \right)$$
$$\left( -{{2 \over 5},{1 \over 5}} \right)$$
$$\left( -{{2 \over 5},-{1 \over 5}} \right)$$
$$\left( {{2 \over 5},-{1 \over 5}} \right)$$