The equation of the common tangent touching the circle (x-3)^2 + y^2 = 9 and the parabola y^2 = 4x above the X-axis is

Step-by-step solution

The equation of a tangent to the parabola y^2 = 4x having slope m is given by y = mx + 1 m , which can be written as mx - y + 1 m = 0 . Since this line is also a tangent to the circle (x-3)^2 + y^2 = 9 , the perpendicular distance from the center of the circle (3, 0) to the line must be equal to its radius 3 . |3m - 0 + 1 m | m^2 + 1 = 3 Squaring both sides: (3m + 1 m )^2 = 9(m^2 + 1) 9m^2 + 6 + 1 m^2 = 9m^2 + 9 1 m^2 = 3 m = 1 3 The point of contact of the tangent on the parabola is ( 1 m^2 , 2 m ) . Since the tan