# Is the following equation an ellipse, circle, parabola, or hyperbola #4x^2-3y^2-48x-6y+129=0#?

##### 1 Answer

Mar 30, 2018

The reference Conic Section tells us that given equation:

Is in the General Cartesian form:

where

The same reference, also. tells us that the determinant,

Compute the determinant:

The determinant is greater than zero, therefore, the conic section is a hyperbola. Here is its graph as proof.

graph{4x^2-3y^2-48x-6y+129=0 [-7.37, 21.11, -7.57, 6.67]}