The equation(s) of the common tangent(s) to the circle x^2+y^2-6x=0 and the parabola, y^2=4xis:

Question

Accepted Answer

Correct answer: B. (b)JEE Main 2019 Since, the equation of tangent to parabola y^2=4x is y= mx+ 1m … (i) The line (i) is also the tangent to circle Then centre of circle = (3 ,0 ) Radius of circle =3 The perpendicular distance from centre to tangent is equal to the radius of circle ∴ (3m+ 1m) 1+m^2=3 ⇒(3m+ 1m)^2=9(1+m)^2 ⇒m= 1 3 Then, from equation (i) : y= 1 3x 3 Hence, 3y=x+3 is one of the required common tangent.

$The equation(s) of the common tangent(s) to the circle x^{2} + y^{2} - 6 x = 0 and the parabola, y^{2} = 4 x is:$

Solution

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