If lengths of chords intercepted by circle {x^2} + {y^2} + 2gx + 2fy = 0 from co-ordinate axes be 10

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10-1.Circle and System of Circles

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If the lengths of the chords intercepted by the circle ${x^2} + {y^2} + 2gx + 2fy = 0$ from the co-ordinate axes be $10$ and $24$ respectively, then the radius of the circle is..

A

$17$

B

$9$

C

$14$

D

$13$

Solution

(d) Given $2\sqrt {{g^2}} = 10$

$\Rightarrow \;|g|\; = 5$

and $2\sqrt {{f^2}} = 24$

$\Rightarrow \;|f|\; = 12$

Therefore, radius is $\sqrt {{5^2} + {{12}^2}} = 13$.

Standard 11

Mathematics

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