Question

7. The radius of a circle with centre \( (a, b) \) and passing through the centre of the circle \( x^{2}+y^{2}-2 g x+f^{2}=0 \) is a) \( \sqrt{(a-g)^{2}+b^{2}} \) b) \( \sqrt{a^{2}+(b+g)^{2}} \) c) \( \sqrt{a^{2}+(b-g)^{2}} \) d) \( \sqrt{(a+g)^{2}+b^{2}} \)

Answer 1

Correct option is a) \(\sqrt{(a-g)^2+b^2}\)

x² + y² 2gx + f² = 0

Center (a,b)

The correct equation are possible from circle

Thus the center here of circle is (g,0).

As circle A passes brought this point.

x² + y² − 2gx = f²

x² + y² − 2gx − f² = 0

Equation of circle A.

(x−g)² + (y−f)² = r²

When the center lies on x−axis, then y we have will be zero.

Taking f = 0