Chapter 9, Problem 8RE

To determine

To write: The equation of the circle in standard form.

Answer to Problem 8RE

The standard equation of the circle is $x^2+y^2=\frac{4}{3}$

Explanation of Solution

Given information:

Given equation of circle is $\frac{3}{4}{x}^2+\frac{3}{4}{y}^2=1$

Consider the given equation of the circle as,

  $\frac{3}{4}{x}^2+\frac{3}{4}{y}^2=1$  ...... (1)

This equation can be re − written as,

  $\begin{array}{c}\frac{3}{4}\left(x^2+y^2\right)=1\\ x^2+y^2=\frac{4}{3}\\ x^2+y^2={\left(\frac{2}{\sqrt{3}}\right)}^2\end{array}$

This implies that the centre of the circle is $\left(0,0\right)$ and radius is $\frac{2}{\sqrt{3}}$ .

Therefore, the standard equation of the circle is $x^2+y^2=\frac{4}{3}$