Write the equation of a circle with endpoints of the diameter at (2, -5) and (-4, 3).?

Question

Write the equation of a circle with endpoints of the diameter at (2, -5) and (-4, 3).
Show your work

Answer 1

u need centre point of a circle to find out its equation.... here u can find the centre by using diameter coordinates

end pts of diameter r (2,-5) and ( -4,3)
circle's centre ll be the mid point between diameter's coordinates....

centre's x-coordinate = (-4+2)/2
= -1
centre's y-coordinate =(3+(-5))/2
= -1
radius of circle ll be
sqrt ( (-4-2)^2 + (3+5)^2)/2 = 5
now eq of circle is given as
(x-x1)^2 + (y-y1)^2 = r^2

so (x+1)^2 + (y +1)^2 = 25

Answer 2

Diameter of the circle = sqrt((2 - (-4))^2 + (-5 - 3)^2) = 10
circle center is P(-1,-1)

The equation is (x + 1)^2 + (y + 1)^2 = 25

Answer 3

Centre (- 1 , -1)
r ² = (- 4 + 1) ² + (3 + 1) ²
r ² = 9 + 16 = 25
(x + 1) ² + (y + 1) ² = 25