Question

How do you find the equation of the circle given center at (5,2) and radius 6√6?

Answer 1

Equation of circle is
`x^2+y^2-10x-4y-187=0`

Explanation:

Let `(x,y)` be a point on circle. As it's distance from center `(5,2)` is equal to radius which is `6sqrt6`, hence

`sqrt((x-5)^2+(y-2)^2)=6sqrt6` or

`(x-5)^2+(y-2)^2)=(6sqrt6)^2` or

`x^2-10x+25+y^2-4y+4=36×6` or

`x^2+y^2-10x-4y+25+4-216=0` or

`x^2+y^2-10x-4y-187=0`