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)