Question

Find the center and radius of the Circle defined by the equation given below.X2+2X+y2+10y=15 ?

Answer 1

The given expression is

$x^2+2x+y^2+10y=15$

First, we divide the coefficients 2 and 10 by 2, then we find their square power

$\begin{gathered} (\frac{2}{2})^2=1^2=1 \\ (\frac{10}{2})^2=5^2=25 \end{gathered}$

We add 25 and 1 to each side of the equation

$\begin{gathered} x^2+2x+1+y^2+10y+25=15+1+25 \\ \end{gathered}$

Now, we factor both trinomials

$(x+1)^2+(y+5)^2=41$

Where h = -1 and k = -5. So, the center is C(-1, -5).

The radius would be

$\begin{gathered} r^2=41 \\ r=\sqrt[]{41}\approx6.4 \end{gathered}$

The radius is 6.4 units long.