Question

Find an equation of the circle that satisfies the given conditions.
Endpoints of a diameter are
P(−2, 1) and Q(8, 9).

Answer 1

equation of a circle\[(x-x_0)^2+(y-y_0)^2=r^2\]

Answer 2

now use the points given to find the radius

Answer 3

the circle has that point as center which is the midpoint of diameter
and radius is distance between diameter ends/2

Answer 4

what?

Answer 5

the equation of a circle is \[(x-x_0)^2+(y-y_0)^2=r^2\\where\space (x_0,y_0)\text{ is the center}\\\text{to find the radius we use the distance formula with the two points given}\]
\[r=\sqrt{(8-(-2))^2+(9-1)^2}=\sqrt{164}\]so you have
\[(x-8)^2+(y-9)^2=164\]

Answer 6

so that is the answer?