Chapter A5.3, Problem 14E

To determine

the given equation is parabola, ellipse or hyperbola.

Answer to Problem 14E

The given equation represents a hyperbola.

Explanation of Solution

Given:

  $25x^2+21xy+4y^2-350x=0$

Calculation:

The given equation

  $25x^2+21xy+4y^2-350x=0$

Comparing with the standard equation,

  $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$

  $\begin{array}{l}A=25\\ B=21\\ C=4\end{array}$

Now discriminate D

  $\begin{array}{l}D=B^2-4AC\\ $ ={(21)}^2-4(25)(4)$=41\end{array}$

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

Conclusion:

Therefore, the given equation represents a hyperbola.