Question

What is the standard form of the equation of a circle with center of a circle is at (-15,32) and passes through the point (-18,21)?

Answer 1

`(x+15)^2+(y-32)^2=130`

Explanation:

The standard form of a circle centred at (a,b) and having radius r is `(x-a)^2+(y-b)^2=r^2`.

So in this case we have the centre, but we need to find the radius and can do so by finding the distance from the centre to the point given :

`d((-15,32);(-18,21))=sqrt((-18-(-15))^2+(21-32)^2)=sqrt130`

Therefore the equation of the circle is

`(x+15)^2+(y-32)^2=130`