# If the length of the chord of the circle $x^2 + y^2 = r^2 \ (r>0)$ along the line $y - 2x = 3$ is r then $r^{2}$ is equal to  Option: 1 Option: 2 12 Option: 3 Option: 4

Length of the chord by the line y = mx + c on the circle$x^2+y^2=a^2$ is

$=2\sqrt{\frac{a^2(1+m^2)-c^2}{1+m^2}}$

Given equation of line, y = 2x +3

and circle $x^2 + y^2 = r^2$

according to question

$\\r=2\sqrt{\frac{r^2(1+4)-9}{1+4}}\\\frac{r^2}{4}=\frac{5r^2-9}{5}\\r^2=\frac{12}{5}$

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