Answer:
[tex](x +10)^2 + (y+6)^2 = 121[/tex]
Step-by-step explanation:
Given equation :
[tex]x^2 + y^2 + 20x +12y + 15 = 0[/tex]
Standard equation of circle :
[tex](x - a)^2 + (y-b)^2 = r^2[/tex]
We will consider the x terms in the equation first to find a.
[tex](x-a)^2 = x^2 - 2ax + a^2[/tex]
-2ax = 20x
a = -20x/2x = -10
a = -10
Next consider the y terms to find b.
[tex](y - b)^2 = y^2 -2by + b^2[/tex]
-2by = 12y
b = -12y /2y = -6
b = -6
[tex](x+10)^2 + (y-6)^2 = x^2 +20x +100 + y^2 +12y + 36[/tex]
[tex]=x^2 + y^2 + 20x +12y + 136\\[/tex]
But the given equation constant is 15. So find the difference between 136 and 15 to find the radius : 136 - 15 = 121
Therefore, radius = √121 = 11
Equation in standard form :
[tex](x +10)^2 + (y+6)^2 = 121[/tex]
