Question

Which of the following equatlons of circle in general form given the center at (5,-8) and radius of 11 units? a. (x-5)²+(y+8)²=121. b. x²+y²-10x+16y-32=0.

c. (x-5)²+(y+8)²=11.
d. x²+y²-10x+16y+32=0.

Answer 1

b

Explanation:

the equation of a circle in general form is

x² + y² + 2gx + 2fy + c = 0

with centre (- g, - f ) and radius
`√(g^2+f^2-c)`

to obtain this form we can write the equation in standard form

(x - h)² + (y - k)² = r²

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

given centre = (5 - 8) and r = 11 , then

(x - 5)² + (y -(- 8) )² = 11² , that is

(x - 5)² + (y + 8)² = 121 ← in standard form

expand factors using FOIL

x² - 10x + 25 + y² + 16y + 64 = 121

x² + y² - 10x + 16y + 89 = 121 ( subtract 121 from both sides )

x² + y² - 10x + 16y - 32 = 0 ← in general form