What is the general form of the equation of a circle with center at (a, b) and radius of length m?

Asked by maham237 @ 02/12/2020 in Mathematics viewed by 370 People

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.

Answered by maham237 @ 02/12/2020

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

What is the general form of the equation of a circle with center at (a, b) and radius of length m?

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