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(D) The length of the intercept made by the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ on the $x$-axis is $2\sqrt{g^2 - c}$.Since the circle passes throug

Vedclass · Accepted Answer

$13$

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(D) The length of the intercept made by the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ on the $x$-axis is $2\sqrt{g^2 - c}$.Since the circle passes through the origin $(c=0)$,the intercept on the $x$-axis is $2\sqrt{g^2} = 2|g|$.Given $2|g| = 10$,we get $|g| = 5$.Similarly,the intercept on the $y$-axis is $2\sqrt{f^2} = 2|f|$.Given $2|f| = 24$,we get $|f| = 12$.The radius of the circle is $r = \sqrt{g^2 + f^2 - c}$.Since $c = 0$,$r = \sqrt{g^2 + f^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$.

If the lengths of the chords intercepted by the circle $x^2 + y^2 + 2gx + 2fy = 0$ from the coordinate axes are $10$ and $24$ respectively,then the radius of the circle is:

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