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

The general form of the equation of a circle with center at (a, b) and radius of length m is B.x2 + y2 + 2ax + 2by + (a2 + b2 − m2)

the standard equation for a circle is: (x-a)^2 + (y-b)^2 = m^2

x-a)^2 + (y-b)^2 = m^2 

means (x-a)(x-a) + (y-b)(y-b) = m^2 then you foil

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = m^2

Answer 2

The generic equation of the circle is given by:
 $(x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2$
 Where,
 r: radius of the circle
 (xo, yo): center of the circle.
 The center of the circle in this case is:
 $(xo, yo): (a, b)$
 The radius of the circle is:
 $r = m$
 Substituting values we have:
 $(x-a) ^ 2 + (y-b) ^ 2 = m ^ 2$
 Rewriting the equation we have:
 $x ^ 2 - 2ax + a ^ 2 + y ^ 2 - 2by + b ^ 2 - m ^ 2 = 0 x ^ 2 + y ^ 2 - 2ax - 2by + a ^ 2 + b ^ 2 - m ^ 2 = 0$
 Answer:
 The general form of the equation of a circle with center at (a, b) and radius of length m is:
 $x ^ 2 + y ^ 2 - 2ax - 2by + a ^ 2 + b ^ 2 - m ^ 2 = 0$
 option A