Question

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.

• A.
• B.
• C.
• D. 3

Answer 1

The correct option is C

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)

$\therefore$ Distance from center to tangent = Radius

i.e.,$\frac{0+0+9}{\sqrt{1+4}}=r=\frac{9}{\sqrt{5}}$