Question

Can someone show me step by step how to do this problem? I'd really appreciate it! :)
Let P(-3,1) and Q(5,6) be two points in the coordinate plane. Find an equation for the circle for which the segment PQ is a diameter.

Answer 1

What is the distance between these points? That will give us the diameter of the circle, which we need.

Answer 2

We also need to know the midpoint, because that is the center.

Answer 3

Do you know how to do these things?

Answer 4

I think so! For the distance, I got sqrt89 and for the midpoint I got (1, 7/2)

Answer 5

is that right so far?

Answer 6

Yes

Answer 7

Okay so do you know the equation of a circle then?

Answer 8

I understand the first part of the equation, but for the r^2 portion, do I just take the square root of 89?

Answer 9

"take" meaning use the square root of 89

Answer 10

so... (x-1)^2 + (y-7/2)^2= sqrt89

Answer 11

well, we need the radius, not diameter.

Answer 12

ohhh. got you.

Answer 13

and it needs to be squared

Answer 14

so the radius is half of 89? or?

Answer 15

ohhhh wait never mind

Answer 16

so its sqrt89/2 squared?

Answer 17

yeah, but when you square a sqrt it isn't a sqrt anymore

Answer 18

right!

Answer 19

so the whole equation is (x-1)^2 + (y+7/2)^2 = 89/4 ?

Answer 20

that looks right

Answer 21

Woohoo! Thank you so much! I really appreciate it! :)