Question

Write an equation in general form of the circle with the given properties. Center at (-8,8); r = 3√3?

Answer 1

The Equation of a Circle

Given a circle of the center at (h,k) and radius r, the equation of the circle can be written as follows:

`(x-h)^2+(y-k)^2=r^2`

The circle has the following properties:

Center at (-8,8). Thus h=-8 and k=8

Radius:

`r=3\sqrt[]{3}`

Substituting in the equation above:

`(x+8)^2+(y-8)^2=(3\sqrt[]{3})^2`

To express this equation in general form, we must expand and operate all the squares:

`x^2+16x+64+y^2-16y+64=3^3(\sqrt[]{3})^2=9\cdot3=27`
`x^2+16x+64+y^2-16y+64-27=0`

Simplifying:

`x^2+y^2+16x-16y+101=0`