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

Answer:

A

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (a, b) and r = m , thus

(x - a)² + (y - b)² = m² ← in standard form

Expand the factors using FOIL and rearrange

x² - 2ax + a² + y² - 2by + b² = m² ( subtract m² from both sides )

x² + y² - 2ax - 2by + (a² + b² - m² ) = 0 ← in general form → A