Question

Statement-1: Tangents are drawn from the point (3, 4) on to the ellipse x²/16 + y²/9 = 1 will be mutually perpendicular. 

Statement-2: The points (3, 4) lies on the circle x² + y² = 25 which is director circle to the ellipse x²/16 + y²/9 = 1.

(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. 

(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1. 

(C) Statement – 1 is True, Statement – 2 is False. 

(D) Statement – 1 is False, Statement – 2 is True. 

Answer 1

Correct option: (a)

Explanation:

will have director circle x² + y² = 16 + 9 

⇒ x² + y² = 25 and we know that the locus of the point of intersection of two mutually perpendicular tangents drawn to any standard ellipse is its director circle.