The equation for common tangent of a hyperbola and a circle centered at origin is y = 2x + 9. What is the radius of the circle.
Here the fact that the line is tangent to a hyperbola need not be used. We have a circle and a line. The perpendicular distance from center of the circle to the tangent will always be equal to the radius.
Centre of circle = (0, 0)
∴ Distance from center to tangent = Radius
i.e.,0+0+9√1+4=r=9√5