Question

Statement-1 : A tangent of the ellipse x² + 4y² = 4 meets the ellipse x² + 2y² = 6 at P & Q. The angle between the tangents at P and Q of the ellipse x² + 2y² = 6 is π/2 

Statement-2 : If the two tangents from to the ellipse x² /a² + y² /b² = 1 are at right angle, then locus of P is the circle x² + y² = a² + b².  

(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:

Equation of PQ (i.e., chord of contact) to the ellipse x² + 2y² = 6 

Any tangent to the ellipse x² + 4y² = 4 is 

i.e., x/2 cosθ + ysinθ = 1 ... (2) 

⇒ (1) & (2) represent the same line h = 3cosθ, k = 3sinθ 

Locus of R (h, k) is x² + y² = 9