If one of the diameters of the circle is a chord of another circle C, whose center is (3,2), then the diameter of the circle C is:

Question

If one of the diameters of the circle $x^{2} + y^{2} - 10 x + 4 y + 13 = 0$ is a chord of another circle C, whose center is (3,2), then the diameter of the circle C is:

Smart Achievers · Accepted Answer

(3)

$2 x + 3 y = 12,$ $3 x - 2 y = 5,$ $13 x = 39 \Rightarrow x = 3,$ $y = 2$

Centre $= C = (5, - 2)$ , radius $= r = \sqrt{25 + 4 - 13} = \sqrt{16} = 4$ , CM $= \sqrt{20},$ CP = 6

Solution

Q.
If one of the diameters of the circle $x^{2} + y^{2} - 10 x + 4 y + 13 = 0$ is a chord of another circle C, whose center is (3,2), then the diameter of the circle C is:

1 $\sqrt{20}$

2 $4$

3 $12$

4 $6 \sqrt{2}$

Ans.
(3)

$2 x + 3 y = 12,$ $3 x - 2 y = 5,$ $13 x = 39 \Rightarrow x = 3,$ $y = 2$

Centre $= C = (5, - 2)$ , radius $= r = \sqrt{25 + 4 - 13} = \sqrt{16} = 4$ , CM $= \sqrt{20},$ CP = 6

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Solution

Q. If one of the diameters of the circle x2+y2-10x+4y+13=0 is a chord of another circle C, whose center is (3,2), then the diameter of the circle C is:

1 20

2 4

3 12

4 62

Ans. (3) 2x+3y=12, 3x-2y=5, 13x=39⇒x=3, y=2 Centre =C=(5,-2), radius =r=25+4-13=16=4, CM =20, CP = 6