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MathematicsCircleFamily of circlesHard2 minPYQ_2021

MathematicsHardnumerical

If one of the diameters of the circle $x^{2} + y^{2} - 2 x - 6 y + 6 = 0$ is a chord of another circle ${}^{'}C^{'}$ , whose center is at $(2, 1)$ , then its radius is_____.

Question diagram: If one of the diameters of the circle x 2 + y 2 - 2 x - 6 y

Answer:

3.00

Solution:

$x^{2} + y^{2} - 2 x - 6 y + 6 = 0$
centre $(1, 3)$

radius $= 2$
Distance between $(1, 3)$ and $(2, 1)$ is $\sqrt{5}$

$∴ {(\sqrt{5})}^{2} + {(2)}^{2} = r^{2}$

$\Rightarrow r = 3$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Family of circles

⏱ 2mℹ️ Source: PYQ_2021

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