The radius of a circle with center (a, b) and | vedclass

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Question

(A) The given circle equation is $x^2 + y^2 - 2gx + f^2 = 0$.Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,the center of this c

Vedclass · Accepted Answer

$\sqrt{(a - g)^2 + b^2}$

Vedclass · Answer

(A) The given circle equation is $x^2 + y^2 - 2gx + f^2 = 0$.Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,the center of this circle is $(g, 0)$.The required circle has center $(a, b)$ and passes through the point $(g, 0)$.The radius $r$ is the distance between the center $(a, b)$ and the point $(g, 0)$.Using the distance formula,$r = \sqrt{(a - g)^2 + (b - 0)^2} = \sqrt{(a - g)^2 + b^2}$.

The radius of a circle with center $(a, b)$ and passing through the center of the circle $x^2 + y^2 - 2gx + f^2 = 0$ is:

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