# How do you identity if the equation #2x^2+12x+18-y^2=3(2-y^2)+4y# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 1 Answer

Set your compass to a radius of 2, put the center at the point

#### Explanation:

Here is a helpful reference Conic Section - General form

Combine all of the terms to be in the general form:

Because

where

Divide both sides of equation [1] by 2:

Add

Set the term middle in the right side of the pattern,

Solve for h:

Substitute the left side on the pattern into equation 3:

Substitute -3 for h in equation [4]:

Set the term middle in the right side of the pattern,

Solve for k:

Substitute the left side of the pattern into equation [5]:

Substitute 1 for k into equation [7]:

Simplify the constant terms:

Write the constant term as a square:

Equation [9] is the standard form of a circle with a center at