Question

Let A=(-1,2) and B=(1,-4). A circle is drawn with AB as diameter. If P(m,n) be a point on the circle,find the relation between m and n.?

Answer 1

See explanation.

Explanation:

From the given information we can calculate that:

• The center of the circle is the midpoint of `AB`, so the center's coordinates are:

`S=((-1+1)/2;(2+(-4))/2)=(0;-1)`

• The radius is equal to:

`r=|SA|=sqrt((0+1)^2+(-1-2)^2)=sqrt(10)`

So the equation is:

`m^2+(n+1)^2=10`

If we move all terms to the left side we get:

`m^2+n^2+2n-9`