What is the equation of the circle if the endpoints of the diameter are (9,-4) and (-3,8)?

(x-3)² + (y+2)² = 72

Step-by-step explanation:

center is halfway between (9,-4) and (-3,8).

average of x-coordinates = (9-3)/2 = 3

average of y-coordinates = (-4+8)/2 = -2

center: (3,-2)

length of diameter = √[(9-(-3))²+(-4-8)²] = √288 = 12√2

radius = 6√2

(x-3)² + (y+2)² = (6√2)² = 72

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47