Chapter 10.6, Problem 4AYU

The eccentricity $e$ of a parabola is ________, of an ellipse it is _________ and of a hyperbola it is _________.

To determine

To fill: The eccentricity e of a parabola is ________, of an ellipse it is _________, and of a hyperbola it is _________.

Answer to Problem 4AYU

$e=1$ for parabola.

$e<1$ for ellipse.

$e>1$ for hyperbola.

Explanation of Solution

Given:

To consider the eccentricity e for parabola, ellipse and hyperbola.

Calculation:

For a conic,

$\frac{d\left(F,P\right)}{d\left(D,P\right)}=e$. Where ‘e’ is the eccentricity of the conic.

if the conic is parabola, then $e=1$.

If the conic is an ellipse, then $e<1$.

If the conic is an hyperbola, then $e>1$.