Need geometry help?

For the equation of circle (x - a)² + (y - b)² = r²
The center is (a, b) and the radius is r.

(a) Incorrect
The equation can be rewritten as: (x - 11)² + [y - (-15)]² = 12²
The center is (11, -15), but NOT (15, -11).

(b) Incorrect
The equation can be rewritten as: (x - 11)² + [y - (-15)]² = 12²
The radius is 12, but NOT 144.

(x - 11)² + (y + 15)² = 144……(1)

(x - h)² + (y - k)² = r²……(2)

Compare equation 1 and 2

h = 11, k = -15, r² = 144

r = √144 = 12

radius of circle (r) = 12.

(x - 11)² + (y + 15)² = 144 = 12²


The typical equation of a circle is: (x - xo)² + (y - yo)² = R² → where:
xo: abscissa of center → 11 in your case
yo: ordinate of center → - 15 in your case
R: radius of circle → 12

The circle is centered at (11 ; - 15)

The equation is (x - a)^2 + (y-b)^2 = r^2 where r is the radius, a the offset from the origin for the x coordinate and b the offset for the y coordinate.
so, centre is (a,b) and radius r
Here: centre is (11,-15) and radius 12 (or diameter = 24)

a. C = (11, -15)

b. r^2 = 144
so r = 12 ... d = 24