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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

Type The Correct Answer In Each Box Use Numerals Instead Of Words If Necessary Use For The Fraction BarsThe Equation Of A Circle Is Given2 Y6x10y180Determine Th class=

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ANSWER

[tex]\begin{gathered} center=(-3,-5) \\ r=4 \end{gathered}[/tex]

EXPLANATION

Given;

[tex]x^2+y^2+6x+10y+18=0[/tex]

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

[tex](x-h)^2+(y-k)^2=r^2[/tex]

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

[tex]\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}[/tex]

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

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