Question

Equation of a common tangent to the circle, x² + y² - 6x = 0 and the parabola, y² = 4x , is: (A) 2√(3) y = 12x + 1 (B) √(3) y = x + 3
(C) 2√(3) y = -x - 12 (D) √(3) y = 3x + 1 [JEE Main 2019]

Answer 1

Answer:

Equation of tangent to parabola is

Y= mx+1/m

m^2 x-my+1=0

It is tangent to circle

Then |3 m^2 +1|/v(m^4+m^2) =3

9m^4+6m^2 +1=9m^4+9m^2

3m^2 =1

m=1/v3

Equation of common tangent is y=1/v3 x+v3

V3y=x+3

Option (B) is correct.