A circle C 1 passes through the origin O and has diameter 4 on the positive x -axis. The line y = 2 x gives a chord O A of a circle C 1 . Let C 2 be the circle with O A as a diameter. If the tangent to C 2 at the point A meets the x -axis at P and y -axis at Q , then Q A : A P is equal to

Step-by-step solution

The centre of the circle C 1 will be 2 , 0 and radius is 2 So, the equation of the circle C 1 is x 2 + y 2 - 4 x = 0 Let θ be the angle made by the line y = 2 x with positive x -axis. i.e. tan θ = 2 Now C 2 is a circle with O A as diameter. So, tangent at A on C 2 is perpendicular to O A Let O A = l ​​​​​​​ ∴ Q A A P = l cot θ l tan θ ⇒ Q A A P = 1 tan 2 θ = 1 4