# What is the standard form of the equation of a circle passing through A(0,1) , B(3,-2) and has its centre lying on the line y=x-2?

##### 1 Answer

Jan 27, 2017

A family of circles

#### Explanation:

The slope of the given line is 1 and the slope of AB is -1.

It follows that the given line should pass through the midpoint of

M(3/2, -1/2) of AB..

And so, any other point C(a, b) on the given line, with

could be the center of the circle.

The equation to this family of circles is

giving

graph{(x+y-1)(x-y-2)(x^2+y^2-4x-1)(x^2+y^2+4y-5)=0x^2 [-12, 12, -6, 6]}