Question

How do you write the equation of a circle with the center (8,7) and radius r=6?

Answer 1

The equation is
`x^2+y^2-16x-14y+77=0`

Explanation:

As a circle is a point that moves so that its distance from a given point (called center) is always same (called radius), we should first calculate the distance of a point `(x,y)` from the center at `(8,7)` and that should be `6`, as radius is given to be `6`.

Hence `sqrt((x-8)^2+(y-7)^2)=6`

Now squaring both sides, we get

`(x-8)^2+(y-7)^2=36` or

`x^2-16x+64+y^2-14y+49=36` or

`x^2+y^2-16x-14y+64+49-36=0` or

`x^2+y^2-16x-14y+77=0`

graph{x^2+y^2-16x-14y+77=0 [-20, 20, -5, 15]}