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 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:

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jul, Evening shift · Q3137

JEE Main 202227 Jul, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

A circle

C_{1}

passes through the origin

\mathrm{O}

and has diameter 4 on the positive

x

-axis. The line

y=2 x

gives a chord

\mathrm{OA}

of circle

\mathrm{C}_{1}

. Let

\mathrm{C}_{2}

be the circle with

\mathrm{OA}

as a diameter. If the tangent to

\mathrm{C}_{2}

at the point

\mathrm{A}

meets the

x

-axis at

\mathrm{P}

and

y

-axis at

\mathrm{Q}

, then

\mathrm{QA}: \mathrm{AP}

is equal to :

JEE Main 2022 · 27 Jul, Evening shift · Q3137

JEE Main 202227 Jul, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

A circle

C_{1}

passes through the origin

\mathrm{O}

and has diameter 4 on the positive

x

-axis. The line

y=2 x

gives a chord

\mathrm{OA}

of circle

\mathrm{C}_{1}

. Let

\mathrm{C}_{2}

be the circle with

\mathrm{OA}

as a diameter. If the tangent to

\mathrm{C}_{2}

at the point

\mathrm{A}

meets the

x

-axis at

\mathrm{P}

and

y

-axis at

\mathrm{Q}

, then

\mathrm{QA}: \mathrm{AP}

is equal to :