Question

Determine which of the following equations represents a circle with a real non-vero radius, a) x2 + y2 + 10x = -30

Answer 1

Given the equation of the circle ;

$x^2+y^2+10x=-30$

Completing the square of the terms of x

so,

$\begin{gathered} (x^2+10x+(\frac{10}{2})^2)+y^2=-30+(\frac{10}{2})^2 \\ \\ (x^2+10x+25)+y^2=-30+25 \\ \\ (x+5)^2+y^2=-5 \end{gathered}$

The general equation of the circle is :

$(x-h)^2+(y-k)^2=r^2$

Comparing the equations together :

$\begin{gathered} r^2=-5 \\ \\ r=\sqrt[]{-5} \end{gathered}$

so, the given equation represents a circle with a non-real radius.