Question

What conic section has the equation `x^2+y^2+12x+8y=48`?

Answer 1

This is an equation for a circle. You begin by reorganizing the terms of the function so that `x` and `x^2` are together and `y` and `y^2` are together.

Next you will have to use the Completing the Square method.

Step 1: Reorder the terms

`x^2+12x+y^2+8y=48`

Step 2: Begin Completing the square

`x^2+12x+y^2+8y=48`

`(12/2)^2=6^2=36`, Value to be added to complete the square

`(8/2)^2=4^2=16`, Value to be added to complete the square

`x^2+12x+36+y^2+8y+16=48+36+16`

`(x^2+12x+36)+(y^2+8y+16)=100`

Factor

`(x+6)^2+(y+4)^2=100`

Solution: Standard form of a Circle.