Question

On the ellipse 4x² + 9y² = 1, the point at which the tangents are parallel to the line 8x = 9y, are

(a) (2/5, 1/5)

(b) (-2/5, 1/5)

(c) (-2/5, -1/5)

(d) (2/5, -1/5)

Answer 1

Correct option 

(b) (-2/5, 1/5)

(d) (2/5, -1/5)

Explanation :

Given, 4x² + 9y² = 1 ....(i)

On differentiating w.r. t. x, we get

The tangent at point (h, k) will be parallel to 8x = 9y, then

Point (h, k ) also lies on the ellipse.

4h² + 9k² = 1 ...(ii)

On putting value of ft in Eq. (ii), we get