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 :

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

1 : 4

2 : 5

1 : 5

1 : 3

answer is A.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} C_{1} : x^{2} + y^{2} - 4 x = 0 \\ \tan θ = 2 \end{array}$

C₂ is a circle with OA as diameter.

So, tangent at A on C₂ is perpendicular to OR

Let $OA = l$

$\begin{array}{l} ∴ \frac{QA}{AP} = \frac{ℓ \cot θ}{ℓ \tan θ} \\ = \frac{1}{\tan^{2} θ} = \frac{1}{4} \end{array}$

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test