Question

Equation of common tangent to circle and parabola

Answer 1

Center of circle: (3,0)
Equation of tangent on parabola:
y=mx+a/m
a=1
y=mx+1/m
Perpendicular Distance from the center of the circle = 3
|3m+1/m|/(1+m)1/2=3
m2=1/3 => m=+1/√3 or -1/√3
As tangent is above x-axis, slope is (+)ve
Therefore, Equation of tangent:
y=x/√3+√3
=> √3y=x+3