A line is a common tangent to the circle(x−3)2+y2=9 and the parabola y2=4x . If the two points of contact (a, b) and (c,d) are distinct and lie in the first quadrant then 2(a+c) is equal to

Equations of the given circle and the parabola are (x−3)2+y2=9;     y2=4x Let y=mx+1m be a  tangent to y2=4x, m2x−my+1=0  is  also tangent to circle having centre at C(3,0), r=3The distance from the centre of the circle and the line is equal to the radius3=3m2+1m4+m29 (m4+m2)=9m4+1+6m29m2=6m2+13m2=1m2=13m=±13Hence the equation of the tangent is y=13x+3⇒x−3y+3=0 For the point of contact, eliminate y and then solve for x(x-3)2+x+332=9  3x-32+x+32=27      3x2+27−18x+x2+6x+9=274x2−12x+9=0   2x-32=0             x=32         andx+332=4xx2+6x+9=12xx2−6x+9=0x=3 ∴2a+c=232+3=3+6=9