Answer:
[tex]x^2 + 10x + y^2 -4y + -7 = 0[/tex]
Step-by-step explanation:
For any circle point with coordinate of center (a,b) and radius r
equation of circle is given by
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
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Given
coordinate of center = (-5,2)
radius = 6
thus, equation of circle can be written by substituting a and b with (-5 ,2) and r =6 as shown below
[tex](x-a)^2 + (y-b)^2 = r^2\\(x-(-5))^2 + (y-2)^2 = 6^2\\x^2 + 10x + 25 + y^2 -4y + 4 = 36\\=>x^2 + 10x + y^2 -4y + 29 = 36\\=>x^2 + 10x + y^2 -4y + 29 -36 = 36 -36\\=>x^2 + 10x + y^2 -4y + -7 = 0[/tex]
Thus, equation of circle is [tex]x^2 + 10x + y^2 -4y + -7 = 0[/tex]
