Equation of a circle

Question

Give the equation whose endpoints of a diameter at (-4,1) and (4, -5)

Answer 1

The center of the circle is the midpoint of any diameter.

So, center = ((-4+4)/2, (-5+1)/2) = (0, -2)

Radius = half the length of the diameter = (1/2)√ [(-4-4)² + (-5-1)²] = 5

Equation of circle has the form (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.

So, we have (x-0)² + (y-(-2))² = 5²

Simplify to get x² + (y+2)² = 25

Answer 2

end points are (-4 , 1 ) and ( 4 , -5 ) .

to find equation .

slop = -5 -1 /4 - - 4 = -3/4.

y = -3/4x + c

1 = -3/4 × -4 + c

c = -2

y = -3/4x -2 .