Question

A circle C1 passes through the origin O and has diameter 4 on the positive x-axis. The line y = 2x gives a chord OA of circle C1. Let C2 be the circle with OA as a diameter. If the tangent to C2 at the point A meets the x-axis at P and y-axis at Q, then QA :AP is equal to

• A. 1 : 4
• B. 1 : 5
• C. 2 : 5
• D. 1 : 3

Answer 1

Answer: (A)

1 : 4

Answer 2

The correct answer is (A) : 1 : 4
Equation of C1
x2 + y2 – 4x = 0
Intersection with
y = 2x
$x^2+4x^2-4x = 0$
$5x^2-4x = 0$
$⇒ x = 0, \frac{4}{5}$
$y = 0, \frac{8}{5}$
$A : (\frac{4}{5}, \frac{8}{5})$

Fig. Circle

Tangent of $C_2$ at $A(\frac{4}{5},\frac{8}{5})$
x+2y = 4
$⇒ P : (4,0), Q : (0,2)$
$QA : AP = 1:4$