Respuesta :
Answer:
The answer to this would be your first option!!
• (x + 10)² + (y+6)2 = 121
Hope this helped, have a blessed day!!
Answer:
• (x + 10)² + (y+6)² = 121
Step-by-step explanation:
For this case we have the following expression:
[tex] x^2 + y^2 +20 x + 12y +15=0[/tex]
And we want to write this on this general way:
[tex] (x-h)^2 +(y-k)^2 = r^2[/tex]
So on this case we need to complete the squares like this:
[tex] x^2 + 20 x + (\frac{20}{2})^2 + y^2 + 12y + (\frac{12}{2})^2 +15 =(\frac{20}{2})^2+(\frac{12}{2})^2[/tex]
Now we can subtract from both sides 15 and we got:
[tex] (x^2 + 20 x +100) + (y^2 + 12y +36) = 100+36 - 15[/tex]
[tex] (x+10)^2 +(y+6)^2 = 121[/tex]
And we can write the last expression like this:
[tex] (x-(-10))^2 +(y-(-6))^2 = 121[/tex]
And if we compare to the general expression we see that:
[tex] h = -10 , k = -6, r=\sqrt{121}=11[/tex]
So the correct option for this case would be:
• (x + 10)² + (y+6)² = 121
