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

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

Step-by-step 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+((6)/(2))^(2)+y^(2)+10y+((10)/(2))^(2)=-18+9+25 \\ (x-3)^2+(y-5)^2=4^2 \end{gathered}`

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