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 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

1 : 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 : 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 : 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $1 : 4$
Equation of $C_{1}$
$x^{2} + y^{2} - 4 x = 0$
Intersection with
$y = 2 x$
$x^{2} + 4 x^{2} - 4 x = 0$
$5 x^{2} - 4 x = 0 \Rightarrow x = 0, \frac{4}{5}$
$y = 0, \frac{8}{5}$
$A : (\frac{4}{5}, \frac{8}{5})$

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

Suggest Corrections

Similar questions

Q. From a point

P

on the circle

C_{1} : x^{2} + y^{2} = 25

, tangents are drawn to the circle

C_{2} : x^{2} + y^{2} = 9

. Let

θ

be the angle made by the line

P O

(

O

is the origin) with positive

x

-axis. If the chord of contact of the circle

C_{2}

is tangent to another circle

C_{3}

which passes through the origin, then locus of center of the circle

C_{3}

Let the tangent to the circle $x^{2} + y^{2} = 25$ at the point $R (3, 4)$ meet the $x$ -axis and $y$ -axis at points $P & Q$ , respectively. If $r$ is the radius of the circle passing through the origin $O$ and having a centre at the incentre of the triangle $O P Q$ , then $r^{2}$ is equal to: