Question

Statement-1 : Two parabolas y² = 4ax and x² = 4ay have common tangent x + y + a = 0 

Statement-2 : x + y + a = 0 is common tangent to the parabolas y² = 4ax and x² = 4ay and point of contacts lie on their respective end points of latus rectum. 

(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: (b)

Explanation:

y² = 4ax 

equation of tangent of slope ‘m’ 

If it touches x² = 4ay then x² = 4a (mx + a/m) 

m³ = -1 ⇒ m = -1 

So y = -x – a ⇒ x + y + a = 0 

(a, -2a) & (-2a, a) lies on it