Chapter 11, Problem 12STP

To determine

To find:The equation which represent the circle.

Answer to Problem 12STP

Equation $(c)x^2=8-y^2$ represent the circle.

Explanation of Solution

Given information:Given equation is:

  $\begin{array}{l}(A)2x^2-y=8\\ (B)2x^2+y^2=8\\ (C)x^2=8-y^2\\ (D)x^2=8+y^2\end{array}$

Calculation:

  $\begin{array}{l}2x^2-y=8\\ 2x^2=y+8\\ x^2=\frac{y}{2}+4\end{array}$

This equation resembles to equation of parabola.

  $\begin{array}{l}2x^2+y^2=8\\ \frac{2x^2}{8}+\frac{y^2}{8}=1\\ \frac{x^2}{4}+\frac{y^2}{8}=1\end{array}$

This equation resembles to equation of ellipse.

  $\begin{array}{l}{x}^2=8-y^2\\ x^2+y^2=8\end{array}$

This equation resembles to equation of circle $x^2+y^2=r^2$ .

  $\begin{array}{l}{x}^2=8+y^2\\ x^2-y^2=8\end{array}$

This equation resembles to equation hyperbola.

Thus, the equation $c$ represent the circle.