A circle C1 passes through the origin O and has diameter 4 on the positive x-axis. The line y =2 x gives a chord OA of a circle C 1. Let C 2 be the circle with OA 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 QA: AP is equal to :

Question

A circle C1 passes through the origin O and has diameter 4 on the positive x-axis. The line y =2 x gives a chord OA of a circle C 1. Let C 2 be the circle with OA 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 QA: AP is equal to : (A) 1: 4 (B) 1: 5 (C) 2: 5 (D) 1: 3

Tardigrade Admin · Accepted Answer

C1: x2+y2-4 x=0 tan θ=2

C 2 is a circle with OA as diameter. So, tangent at A on C 2 is perpendicular to OR

$1 : 4$

$1 : 5$

$2 : 5$

$1 : 3$

$C_{1} : x^{2} + y^{2} - 4 x = 0$
$tan θ = 2$

$C_{2}$ is a circle with $O A$ as diameter.
So, tangent at $A$ on $C_{2}$ is perpendicular to $OR$

Q. 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 a 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 :

1:4

1:5

2:5

1:3

C1​:x2+y2−4x=0 tanθ=2 C2​ is a circle with OA as diameter. So, tangent at A on C2​ is perpendicular to OR

$1 : 4$

$1 : 5$

$2 : 5$

$1 : 3$

$C_{1} : x^{2} + y^{2} - 4 x = 0$
$tan θ = 2$

$C_{2}$ is a circle with $O A$ as diameter.
So, tangent at $A$ on $C_{2}$ is perpendicular to $OR$