Question

Graph the equation with a diameter that has endpoints at (-2,-2) and (4,2)

Answer 1

Okay so by distance formula you can find out the diameter of the circle = whole rt (6^2 + 4^2)
= rt 52 = 2 rt 13
Thus the radius of the circle would be half of that = rt 13 :)
Now we know 2 points on the circle and we know the radius and we CAN find out the center of the circle ,which will be the center of the diameter also, by midpoint formula!
Thus the center of the circle would be = (1,0)
Now you know the equation of the circle = (x - x1)^2 + (y-y1)^2 = r^2
SO we know r^2 and (x1,y1) = (1,0)!
Thus the equation of the circle would be = (x-1)^2 + y^2 = 13 [SIMPLIFY THAT]
SOLVED :)
Distance formula = whole root (x2-x1)^2 + (y2-y1)^2
Midpoint formula = (xm,ym) = [(x1 + x2)/2,(y1+y2)/2]

Answer 2

Could I write the equation as (x-1)^2 + (y-0)^2?

Answer 3

is = r^2 ?
YES YOU CAN :) but simplify it at the end! :D

Answer 4

and what would be two other points on the circle be? how do i simplify that?

Answer 5

You don;t actually need the other 2 points to find the EQUATION of the circle!
Because in a circle equation all you need is centre and the radius!
The other 2 points although ARE important in this question to find out the length of the diameter and the radius and the center of the circle :)

Answer 6

I have to have four points, how do i find more points

Answer 7

Did you get it?

Answer 8

I think, the equation is (x-1)^2+y^2=13 or does it equal 12?

Answer 9

No no when we open (x-1)^2 we get = x^2 - 2x +1
Thus the FINAL equation = x^2 - 2x + y^2 = 12 [BEcause 1 shifts to the other side]

Answer 10

is that the equation of the circle

Answer 11

YES THE FINAL EQUATION :)

Answer 12

And you can even verify it by putting in your 4 points

Answer 13

my circle looks weired

Answer 14

Yeah? Let me just check it!

Answer 15

THIS IS WHAT IT SHOULD LOOK LIKE :)
Just don't use the other 2 points that I gave you okay?

Answer 16

BUT I HOPE YOU GOT THE STEPS TO FIND THE EQUATION!
THE Equation is crect and so are the points!
Just cross check it with the graph attached! :D