Question

If the center of a circle is at (3,-8) and the diameter is 10 fine the following:

a.) radius

b.) Equation of the circle

Answer 1

see explanation

Explanation:

(a)

the radius r of a circle is half the diameter , so

r = 10 ÷ 2 = 5

(b)

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 the radius

here (h, k ) = (3, - 8 ) and r = 5 , then

(x - 3)² + (y - (- 8) )² = 5² , that is

(x - 3)² + (y + 8)² = 25 ← equation of circle