Question

determine the shape of the graph represented by this equation: -x^2 + 4y^2 - 6x -48y + 139= 0 Ellipse or hyperbole

Answer 1

Hyperbole.

Step-by-step explanation

The given equation is

`- {x}^(2) + 4 {y}^(2) - 6x - 48y + 139 = 0`

We use the sign of the quadratic terms to determine whether the conic is a hyperbole or an ellipse.

Since the sign of the coefficient of the quadratic terms are opposite, the conic is a hyperbole.

Answer 2

The graph of the given function yields a hyperbola shown in the attached image below