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

17

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9

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14

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13

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Solution

The correct option is D $13$
$\begin{matrix} x^{2} + y^{2} + 2 g x + 5 f y = 0 2 \sqrt{g^{2}} = 10 \Rightarrow g^{2} = 25 2 \sqrt{f^{2}} = 24 \Rightarrow f^{2} = 144 r a d i u s = \sqrt{g^{2} + f^{2}} = \sqrt{169} = 13 u n i t s H e n c e, t h e o p t i o n D i s t h e c o r r e c t a n s w e r . \end{matrix}$

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Similar questions

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

Q. Length of the tangent drawn from any point on the circle

x^{2} + y^{2} + 2 g x + 2 f y + c_{1} = 0

to the circle is

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

Q. The length of the tangent drawn from any point on the circle

x^{2} + y^{2} + 2 g x + 2 f y + p = 0

to the circle

x^{2} + y^{2} + 2 g x + 2 f y + q = 0

is:

Q. If the circle

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

bisects the circumference of the circle

x^{2} + y^{2} + 2 g_{1} x + 2 f_{1} y + c_{1} = 0

then the length of the common chord of the circles is

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If the lengths of the chords intercepted by the circle x2+y2+2gx+2fy=0 from the coordinate axes are 10 and 24 units, respectively, then the radius of the circle is:

The correct option is D 13x2+y2+2gx+5fy=02√g2=10⇒g2=252√f2=24⇒f2=144radius=√g2+f2=√169=13unitsHence,theoptionDisthecorrectanswer.

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