Question

If y = m₁x + c₁ and y = m₂x + c₂ , m₁  ≠ m₂ are two common tangents of circle x² + y² = 2 and parabola y² = x, then the value of 8|m₁m₂ | is equal to

(A) 3 + 4√2

(B) -5 + 6√2

(C) -4 + 3√2

(D) 7 + 6√2

Answer 1

Correct option is (C) -4 + 3√2

C₁ : x² + y² = 2

C₂ : y² = x

Let tangent to parabola be y = mx + 1/4m. It is also a tangent of circle so distance from centre of circle (0, 0) will be √2.