Question

How do you graph `x^2+y^2+6x-16y+48=0`?

Answer 1

Rearrange and group the terms to get the expression into the standard form of one of the conics - in this case a circle. You can then identify the key points that you need to be able to graph it.

Explanation:

`x^2 + 6x +y^2 -16y +48 = 0`

`(x+3)^2 -9 + (y - 8)^2 -64 +48 = 0`

`(x+3)^2 +(y-8)^2 =73-48 = 25`

This is now recognisably a circle in the form

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

where `(h,k)` is the centre of the circle and `r` is the radius.

In this example `(-3,8)` is the centre and the radius is `5`