Answer:
[tex](x-3)^2+ (y+5)^2=10[/tex]
Step-by-step explanation:
Given the equation of the circle: [tex]x^2 + y^2 - 6x + 10y + 24 = 0[/tex]
We wish to express it in a Standard form:
We begin by re-arranging:
[tex]x^2 - 6x + y^2 + 10y = - 24[/tex]
Next, divide the coefficient of x by 2, square it and add it to both sides.
Do the same for y.
[tex]x^2 - 6x +(-3)^2+ y^2 + 10y+5^2 = - 24+(-3)^2+5^2[/tex]
Next, we factorize
[tex](x-3)^2+ (y+5)^2 = - 24+9+25\\(x-3)^2+ (y+5)^2=10[/tex]
This is the standard form.
