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

12

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\frac{24}{5}

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\frac{9}{5}

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\frac{12}{5}

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Solution

The correct option is D $\frac{12}{5}$

$A B = r = 2 A M = 2 \sqrt{r^{2} - 9 / 5}$
$\Rightarrow r^{2} - \frac{9}{5} = \frac{r^{2}}{4}$
$\Rightarrow \frac{3 r^{2}}{4} = \frac{9}{5}$
$\Rightarrow r^{2} = \frac{12}{5}$

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If the length of the chord of the circle, x2+y2=r2 (r>0) along the line,y−2x=3 is r, then r2 is equal to

The correct option is D 125 AB=r=2AM=2√r2−9/5 ⇒r2−95=r24 ⇒3r24=95 ⇒r2=125

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

The correct option is D $\frac{12}{5}$

$A B = r = 2 A M = 2 \sqrt{r^{2} - 9 / 5}$
$\Rightarrow r^{2} - \frac{9}{5} = \frac{r^{2}}{4}$
$\Rightarrow \frac{3 r^{2}}{4} = \frac{9}{5}$
$\Rightarrow r^{2} = \frac{12}{5}$