# How do you determine circle, parabola, ellipse, or hyperbola from equation #4x^2 + 9y^2 - 16x +18y -11 = 0#?

##### 2 Answers

See below

#### Explanation:

Here's an easy way:

**-If the coefficients on #x^2# and #y^2# match, it is a circle**

**-If there is only one squared term, it is a parabola**

**-If one of the squared terms has a negative coefficient, it is a hyperbola**

**-If the coefficients on #x^2# and #y^2# don't match but they still have coefficients that either both positive or both negative, it is a ellipse**

This is an ellipse, let's put in it's standard form:

This is a horizontal ellipse

Ellipse

#### Explanation:

Compare the given general quadratic equation:

Now, the determinant

hence, the given quadratic equation:

Now, using second determinant

Given quadratic equation

Above ellipse has center at