Chapter A5.3, Problem 15E

To determine

the given equation is parabola, ellipse or hyperbola.

Answer to Problem 15E

The given equation represents a ellipse.

Explanation of Solution

Given:

  $6x^2+3xy+2y^2+17y+2=0$

Calculation:

The given equation

  $6x^2+3xy+2y^2+17y+2=0$

Comparing with the standard equation,

  $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$

  $\begin{array}{l}A=6\\ B=3\\ C=2\end{array}$

Now discriminate D

  $\begin{array}{l}D=B^2-4AC\\ $ ={(3)}^2-4(6)(2)$=-39\end{array}$

Since D>0, the given equation represents aellipse.

Conclusion:

Therefore, the given equation represents a ellipse.