equation of the circle?

Question

It says, write the equation of the circle whose diameter goes from A(7,-2) to B(1,12)

a) Write the equation in the standard form
b)Write the equation in the general form

Answer 1

OK, first you have to find the distance between the points.
distance formula is
(x-x)squared + (y-y) squared = distance squared.
so that means
**(7-1)squared + (-2-12)squared= d squared**
6 squared + -14 squared = d squared
36 +196 = d squared
232 = d squared
square root of 232 = d
about 15.23 = distance = diameter
now, if you want to find circumference, you do this
C = pi times **(insert the equation above that is starred)
if you want area you do this
A = pi times 1/2(the starred equation SQUARED)
if you use a good calculator it will have a pi button, if not insert 3.14

Answer 2

The center of the circle would be the midpoint of the diagonal:
((1 + 7)/2, (12 - 2)/2) = (4, 5)
The radius would be the distance from the center to either endpoint:
√((4-1)^2 + (5 - 12)^2)) = √58
So standard form would be:
(x - 4)^2 + (y - 5)^2 = 58
Multiply and combine terms for general form.

Answer 3

to find the center, find the midpoint (average of x and average of y), and you find it is (4,5).

The equation in standard form is:
(x-4)^2 + (y-5)^2 = r^2

r^2=58

r=7.616

(x-4)^2 + (y-5)^2 = 58