Question

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

Explanation :

The ellipse is

x²(1/4) + y²(1/9) = 1

The tangent at (x₁, y₁) is 4xx₁ + 9yy₁ = 1 which is parallel to 9y = 8x. This implies

-4x₁/9y₁ = 8/9

x₁ = -2y₁  ...(1)

Since (x₁, y₁) lies on the ellipse, we have

4x₁² + 9y₁² = 1  ...(2)

Substituting x₁ = −2y₁ in Eq. (2), we get

Therefore, the points are

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