Question

What is the standard form of the equation of a circle with centre (1,7) passing through the point (-4,-5)?

Answer 1

`(x-1)^2+(y-7)^2=169`

Explanation:

The distance from the point (1,7) to the point (-4,-5) is
`sqrt((-4-1)^2+(-5-7)^2)=13`.

Thus the radius of the circle is 13.

But the general form of a circle centred at (a,b) and having radius r is given by
`(x-a)^2+(y-b)^2=r^2`

Therefore the equation for this particular circle is

`(x-1)^2+(y-7)^2=169`