Writing standard form equation for a circular when given diameter’s endpoints

Question

Endpoints are (-7.4) and (3,8)

please show every step, we didn’t go over this

Answer 1

The standard equation for a circle in relation to it's diameter is Circumference = diameter x pi or C = D x pi

So how do you find the diameter from coordinates? It is easiest to remember by drawing them or picturing them on a graph so that you'll never have to remember this (coordinate difference) formula again, but it's just this:

We get distance between 2 points on a graph using the Pythagorean Theorem (This one you will have to remember) a² + b² = c² with c being the length of the side of the triangle opposite the right angle.

So to get the distances from the other two sides from graphic coordinates is a = x1-x2 and b=y1-y2 or in this case -7-3,4-8 which equal -10,-4. These are our lengths for a and b. The + or - sign doesn't matter as we are only interested in the absolute distance between the points. So since a² = b² =c², c = √a2+b2 and since c is the diameter of the circle we are interested in, C = √10²+4² x pi , = √116 x pi, =10.77 x 3.14 = 33.83

So: C = pi x D

C = pi x √(x₁-x₂)+(y₁-y₂)

Answer 2

With the endpoints use the midpoint formula to find the center.

mid-point = (-7+3)/2 , (4+8)/2

mid-point = center = (-4/2 , 12/2) = (-2 , 6)

With the End points you can also find the radius using the distance formula and then divide the distance by "2"

d= √((3--7)² + (8-4)²)

d= √(10² + 4²)

d= √116

d/2 = radius = (√(\116)/2

Simplify

radius = √29

Now you have everything you need

center = (-2 , 6)

Radius = √29

Substitute them in the standard form of a circle:

(x+2)² + (y-6)² = (√29)²

(x+2)² + (y-6)² = 29