Question

the points (-6,8) and (6,-8) are the endpoints of the diameter of a circle. Write the standard form of the equation of the circle

Answer 1

So, what do we need to define the standard form?
(x - h)^2 + (y - k)^2 = r^2
(h, k) and r look like the priority here.

Finding the center is just thinking about where it lies on the diameter.
Finding the radius is the distance from that center to an endpoint of the diameter. (One-half the diameter).

Answer 2

use the midpoint formula to get the center coordinates
use the distance formula to get the radius
access is leading you there

Answer 3

what does midpoint formula look like?

Answer 4

It's basically like the average of the x values and the average of the y-values:
\( \Large M = \left( \frac{x_1 + x_2}{2} , \ \frac{y_1 + y_2}{2} \right) \)

Answer 5

ok so once i get the coordinates. i use distance which looks like?

Answer 6

I am sorry, i just don't remember. Thanks for your help.

Answer 7

\[ D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Geometrically, this is just Pythagorean Theorem in a coordinate grid