The circle represented by the equation x^2 + | vedclass

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Question

(A) The general equation of a circle is given by $x^2 + y^2 + 2gx + 2fy + c = 0$.The radius $R$ of this circle is given by the formula $R = \sqrt{g^2

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$g^2 + f^2 = c$

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(A) The general equation of a circle is given by $x^2 + y^2 + 2gx + 2fy + c = 0$.The radius $R$ of this circle is given by the formula $R = \sqrt{g^2 + f^2 - c}$.$A$ circle is defined as a point circle when its radius is equal to zero.Setting the radius to zero,we get $\sqrt{g^2 + f^2 - c} = 0$.Squaring both sides,we obtain $g^2 + f^2 - c = 0$,which simplifies to $g^2 + f^2 = c$.

The circle represented by the equation $x^2 + y^2 + 2gx + 2fy + c = 0$ will be a point circle,if

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