Question

What is the general form of the equation of a circle with center at (a, b) and radius of length m?. A. x2 + y2 − 2ax − 2by + (a2 + b2 − m2) = 0 . . B.x2 + y2 + 2ax + 2by + (a2 + b2 − m2) = 0. C. x2 + y2 − 2ax − 2by + (a + b − m2) = 0. D. x2 + y2 + 2ax + 2by + a2 + b2 = -m2.

Answer 1

$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{a}{ h},\stackrel{b}{ k})\qquad \qquad radius=\stackrel{m}{ r} \\\\\\ \boxed{(x-a)^2+(y-b)^2=m^2}\\\\ -------------------------------\\\\ (x^2-2ax+a^2)+(y^2-2yb+b^2)=m^2 \\\\\\ x^2-2ax+a^2+y^2-2yb+b^2-m^2=0 \\\\\\ x^2+y^2-2ax-2yb+(a^2+b^2-m^2)=0$