Question

Give the properties for the equation x^2 + y^2 + 8x - 2y +15 = 0Radius√242

Answer 1

Given equation is

`x^2+y^2+8x-2y+15=0`

Convert this equation into standard form of circle equation.

`\begin{gathered} x^2+2(4)x+4^2+y^2_{}+2(-1)y+1+15-16-1=0 \\ (x+4)^2+(y-1)^2-2=0 \end{gathered}`

On simplifying,

`\begin{gathered} (x+4)^2+(y-1)^2=2 \\ (x+4)^2+(y-1)^2=(\sqrt[]{2})^2 \end{gathered}`

Hence the radius of the circle is

`\sqrt[]{2}`