Question

The equation of circle having a diameter with endpoints (-2, 1) and (6, 7) is
a.(x - 4)² + (y - 3)² = 25

b.(x - 2)² + (y - 4)² = 25

c.(x - 2)² + (y - 4)² = 100

Answer 1

Okay first we need to use the distance formula to find the length of the diameter, since we will need the center and radius.
\(d=\sqrt{(x2-x1)^2+(y2-y1)^2}\)
Here x1=-2, x2=6, y1=1, and y2=7
What do you get when you plug these in?

Answer 2

i got 10

Answer 3

Yep I got that too! Now we know that length of the diameter is 10, so the radius is half of that which is 5. So now that we have found the radius, we can find the center by using the midpoint formula: \(\large\frac{(x1+x2)}{2},\frac{(y2+y1)}{2}\) you can use the same values for the x1 and stuff