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If the length of the chord of the circle $x^{2} + y^{2} = r^{2}$ along the line $y - 2 x = 3$ is $r,$ then $r^{2}$ is equal to

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Correct option is C

The length of the chord of the circle x2 + y2 = r2 along the line y = mx + c is given by 2r21+m21+m2−c2Here, m = 2 and c = 3. Therefore, r=2r2(1+4)−91+4⇒ r=25r2−95⇒5r2=20r2−36⇒r2=3615=125

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If the length of the chord of the circle x2 + y2 = r2 along the line y - 2x = 3 is r, then r2 is equal to

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Ready to Test Your Skills?

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If the length of the chord of the circle $x^{2} + y^{2} = r^{2}$ along the line $y - 2 x = 3$ is $r,$ then $r^{2}$ is equal to