Chapter A5.1, Problem 13E

To determine

To find: the given conic section focus, vertices and asymptotes.

Answer to Problem 13E

The given conic section Centre to focus distance $c=1$ , focus $(\pm 1,0)$ , vertices $(\pm 2,0)$ .

Explanation of Solution

Given:

  $\frac{x^2}{2}+{\frac{y}{1}}^2=1$

Calculation:

The given conic section Centre to focus distance, focus, vertices and asymptotes is calculated below

  $\frac{x^2}{2}+{\frac{y}{1}}^2=1$

Comparing the equation with the standard equation

  $\frac{x^2}{a^2}+{\frac{y}{b^2}}^2=1$

Centre to focus distance : $\begin{array}{l}\\ c=\sqrt{a^2-b^2}\\ c=1\end{array}$

focus : $\begin{array}{l}\\ (\pm c,0)\\ (\pm 1,0)\end{array}$

Vertices : $\begin{array}{l}\\ (\pm a,0)\\ (\pm 2,0)\end{array}$

Conclusion:

Therefore, thegiven conic section Centre to focus distance $c=1$ , focus $(\pm 1,0)$ , vertices $(\pm 2,0)$ .