Question

The diameter of a circle has endpoints (2,-6) and (-4,-16).

Answer 1

Answer:

$(x + 1)^{2} + (y + 11)^{2} = 34$

Step-by-step explanation:

First find the midpoint of the segment  from (2, -6) to (-4, -16)

((2 - 4)/2, (-6 - 16)/2)

(-2/2, -22/2)

(-1, -11) is the midpoint and is the center of the circle

Now find the distance between the 2 given points and divide by 2 to get the radius of the circle

d = $\sqrt{(2 + 4)^{2} + (-6 + 16)^{2} }$

  = $\sqrt{6^{2} + 10^{2} }$

  = $\sqrt{36 + 100}$

  = $\sqrt{136}$

r = $\sqrt{136}$/2

$r^{2}$ = 136/4 = 34

Equation of circle with center at (-1, -11) and radius = $\sqrt{34}$ is

$(x + 1)^{2} + (y + 11)^{2} = 34$