Question

If equation of a circle is x^2 + y^2 + 6x + 4y + 10 = 1 What is this equation written in its standard form?

Answer 1

$\text{The equation of a circle in standard form:}\\\\(x-h)^2+(y-k)^2=r^2\\\\(h,\ k)-center\\r-radius\\---------------------------\\\\Use\ (a+b)^2=a^2+2ab+b^2\\\\---------------------------$

$x^2+y^2+6x+4y+10=0\qquad\text{subtract 10 from both sides}\\\\x^2+6x+y^2+4y=-10\\\\x^2+2x\cdot3+y^2+2y\cdot2=-10\qquad\text{add}\ 3^2\ \text{and}\ 2^2\ \text{to both sides}\\\\(x^2+2x\cdot3+3^2)+(y^2+2y\cdot2+2^2)=-10+3^2+2^2\\\\(x+3)^2+(y+2)^2=-10+9+4\\\\\boxed{(x+3)^2+(y+2)^2=3}$