Chapter A5.3, Problem 36E

To determine

the given equation is parabola, ellipse or hyperbola.

Answer to Problem 36E

The given equation represents a hyperbola.

Explanation of Solution

Given:

  $AC<0$

Calculation:

The given standardequation

  $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$

Now,

  $\begin{array}{l}AC<0\\ 4AC<0\\ -4AC>0\end{array}$

Now discriminate D

  $\begin{array}{l}D=B^2-4AC\\ B^2-4AC>0\\ \text{D>}0\end{array}$

Since D>0, the given equation represents a hyperbola.

Conclusion:

Therefore, the given equation represents a hyperbola.