Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use/ for the fraction bar(s).The equation of a circle is given.2+ y²+6x+10y+18=0Determine the center and radius of the circle.) and the radius of the circle isunits.The center of the circle is at (ResetNext

Answer 1

ANSWER

$\begin{gathered} center=(-3,-5) \\ r=4 \end{gathered}$

EXPLANATION

Given;

$x^2+y^2+6x+10y+18=0$

The standard equation of circle of a circle centered at (h,k) with radius r is;

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

Re-write the given equation in the standard form, we have;

$\begin{gathered} x^{2}+y^{2}+6x+10y+18=0 \\ x^{2}-6x+(\frac{6}{2})^{2}+y^{2}+10y+(\frac{10}{2})^{2}=-18+9+25 \\ (x-3)^2+(y-5)^2=4^2 \end{gathered}$

Hence, h=-3, k=-5, radius is 4