Question

What is the standard form equation of the circle given below?y2 + 2x + x2 = 24y − 120

Answer 1

Given the standar form of the circle

`(x-h)^2+(y-k^2)=r^2`

and given the expression

`y^2+2x+x^2=24y−120`
`y^2+2x+x^2-24y+120=0`
`(x^2+2x)+(y^2-24y)+120=0`
`(x^2+2x+1)+(y^2-24y+144)-25=0`
`(x+1)^2+(y-12)^2=25`
`(x-(-1))^2+(y-12)^2=5^2`

the circumference have r=5

and center in (-1 , 12)