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

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Solution

The correct option is D
13

Given $2 \sqrt{g^{2}} = 10 \Rightarrow | g | = 5$

and $2 \sqrt{f^{2}} = 24 \Rightarrow | f | = 12$

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

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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. 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

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and

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units, respectively, then the radius of the circle is:

Q. If a chord of a circle

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Q. The chord of the circle

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makes equal intercepts of length

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on the co-ordinate axes then

| l | < 8

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

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If the lengths of the chords intercepted by the circle x2+y2+2gx+2fy=0 from the co-ordinate axes be 10 and 24 respectively, then the radius of the circle is

The correct option is D 13 Given 2√g2=10⇒|g|=5 and 2√f2=24⇒|f|=12 Therefore, radius is √52+122=13

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

The correct option is D
13

Given $2 \sqrt{g^{2}} = 10 \Rightarrow | g | = 5$

and $2 \sqrt{f^{2}} = 24 \Rightarrow | f | = 12$

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