the equation of a circle in general form is x squared + y squared + 20x + 12 y + 15 equals 0what is the equation of the circle in standard form ​

Accepted Solution

Answer: [tex](x+10)^2+(y+6)^2=121[/tex]Step-by-step explanation: The equation of a circle in the general form is: Β [tex]ax^{2}+by^2+cx+dy+e=0[/tex] The equaton of Β a circle in standard form is: [tex](x-h)^2+(y-k)^2=r^2[/tex]Where the center is at (h, k) and r is the radius To write the equation of a circle from general form to standard form, you must complete the squaare, as you can see below: 1- Given the equation in general form: [tex]x^{2}+y^2+20x+12y+15=0[/tex] 2- Complete the square: -Group the like terms and move the constant to the other side. - Complete the square on the left side of the equation. - Add the same value to the other side. Then you obtain: [tex](x^{2}+20x)+(y^2+12y)=-15\\(x^2+20x+(\frac{20}{2})^2)+(y^2+12y+(\frac{12}{2})^2)=-15+(\frac{20}{2})^2+(\frac{12}{2})^2\\\\(x+10)^2+(y+6)^2=-15+100+36\\(x+10)^2+(y+6)^2=121[/tex]