Geometry – Equation of a Family of Circles Through Two Points

Question

We have to write the equation of a family of circles passing through two given points $(x_1,y_1)$ & $(x_2, y_2)$

From these points , I only know one circle that is

$$(x_1-x)(x_2-x)+(y-y_1)(y-y_2)=0$$

But now how Can I write other equations .

Answer 1

Family of circle passing through two given points $A(x_1, y_1)$ and $B(x_2, y_2)$.

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