Chapter A5.3, Problem 16E

To determine

the given equation is parabola, ellipse or hyperbola.

Answer to Problem 16E

The given equation represents a parabola.

Explanation of Solution

Given:

  $3x^2+12xy+12y^2+435x-9y+72=0$

Calculation:

The given equation

  $3x^2+12xy+12y^2+435x-9y+72=0$

Comparing with the standard equation,

  $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$

  $\begin{array}{l}A=3\\ B=12\\ C=12\end{array}$

Now discriminate D

  $\begin{array}{l}D=B^2-4AC\\ $ ={(12)}^2-4(3)(12)$=0\end{array}$

Since D=0, the given equation represents a parabola.

Conclusion:

Therefore, the given equation represents a parabola.