The equation of the family of circles passing | vedclass

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(D) The family of circles passing through the intersection of a circle $S = 0$ and a line $P = 0$ is represented by the equation $S + \lambda P = 0$,w

Vedclass · Accepted Answer

All of these

Vedclass · Answer

(D) The family of circles passing through the intersection of a circle $S = 0$ and a line $P = 0$ is represented by the equation $S + \lambda P = 0$,where $\lambda$ is a parameter.Since $\lambda$ can be any real number,$S - \lambda P = 0$ is also a valid representation (by replacing $\lambda$ with $-\lambda$).Additionally,if we consider the form $\lambda S + P = 0$,it represents the family of circles provided $\lambda 
eq 0$ and the line is treated as a degenerate circle.Thus,all the given forms can represent the family of circles under appropriate conditions.Therefore,the correct option is $D$.

The equation of the family of circles passing through the point of intersection of a circle $S = 0$ and a line $P = 0$ is given by:

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