Chapter 11, Problem 5RCC

To determine

To find: Whether the non degenerate conic is a parabola (or) an ellipse (or) a hyperbola

Answer to Problem 5RCC

If $\text{AC > 0}\to \text{ellipse}$

  $\text{AC < 0}\to \text{Hyperbola}$

  $\text{AC = 0;}\frac{\text{A}}{\text{C}}\text{= 0}\to \text{Parabola}$

The given non − degenerate conic is Parabola.

Explanation of Solution

Given information:

A non degenerate conic; $A{x}^2+C{y}^2+Dx+Ey+F=0$

Calculation:

To determine the type of conic, we have to consider product of coefficient of $x^2$ and coefficient of $y^2$

Here; coefficient of $x^2=A$

Coefficient of $y^2=C$

If $A\times C>0$

Then the given non − degenerate conic is ellipse.

If $A\times C<0$

Then the given non − degenerate conic is Hyperbola.

If $\text{AC = 0;}\frac{\text{A}}{\text{C}}\text{= 0}\to \left(\text{not both =0}\right)$

Then, the given non − degenerate conic is Parabola.