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+((10)/(2))^2)+y^2=-30+((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.