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

Sep 13, 2014

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

${x}^{2} + 12 x + {y}^{2} + 8 y = 48$

Step 2: Begin Completing the square

${x}^{2} + 12 x + {y}^{2} + 8 y = 48$

${\left(\frac{12}{2}\right)}^{2} = {6}^{2} = 36$, Value to be added to complete the square

${\left(\frac{8}{2}\right)}^{2} = {4}^{2} = 16$, Value to be added to complete the square

${x}^{2} + 12 x + 36 + {y}^{2} + 8 y + 16 = 48 + 36 + 16$

$\left({x}^{2} + 12 x + 36\right) + \left({y}^{2} + 8 y + 16\right) = 100$

Factor

${\left(x + 6\right)}^{2} + {\left(y + 4\right)}^{2} = 100$

Solution: Standard form of a Circle.