1. Tardigrade
  2. Question
  3. Mathematics
  4. If the length of the chord of the circle, x 2+ y 2= r 2( r >0) along the line, y -2 x =3 is r, then r2 is equal to :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If the length of the chord of the circle, $x ^{2}+ y ^{2}= r ^{2}( r >0)$ along the line, $y -2 x =3$ is $r$, then $r^{2}$ is equal to :

JEE MainJEE Main 2020Conic Sections

Solution:

Let chord
$AB = r$
$\because \Delta AOM$ is right angled triangle
$\therefore OM =\frac{ r \sqrt{3}}{2}=$ perpendicular distance of line
image
AB from (0,0)
$\frac{ r \sqrt{3}}{2}=\left|\frac{3}{\sqrt{5}}\right|$
$r^{2}=\frac{12}{5}$