Question

Write an equation for a circle with a diameter of that has endpoints at (8,7) and (-4,-3). Round to the nearest tenth if necessary.

Answer 1

I think the answer's (x-y)^2+(y-2)^2=244 is this accurate?

Answer 2

What do endpoints mean?

Answer 3

Does it mean that the line segment from (-4, -3) to (8, 7) is a diameter?

Answer 4

yes

Answer 5

Well, that's good for us :)
the endpoints give us the radius AND the center of the circle
Shall I demonstrate, or can you do it from here?

Answer 6

Well. Am I right or am I wrong? :P

Answer 7

well, actually, no, you have an (x - y) in your equation, maybe you'd like to correct that :P

Answer 8

Unless you did that on purpose, though

Answer 9

Oops. :P

Answer 10

Give me a minute, please.

Answer 11

(x+2)^2+(y+2)^2 = 61

There, is that better? :)

Answer 12

might I ask how you got it?

Answer 13

I really am bad at articulating stuff like that, sorry.

Answer 14

My mind just... cannot transfer that into words. Plus, English isn't my native language.

Answer 15

Well, that's ok, but I'd have to say, your equation was wrong...
would you like me to show you the steps to the correct one, or would you prefer to do it yourself?

Answer 16

I'd love to learn how to answer this question properly and accurately, yes. :)

Answer 17

So you have your endpoints... Let's use them to get the diameter of the circle, with our tool called the distance formula :D
The distance from (-4, -3) to (8, 7) is given by
\[\sqrt{(7+3)^{2} + (8+4)^{2}}\]
Did you do this?

Answer 18

What....

Answer 19

I don't know how to find the square root of that.

Answer 20

But you do get
\[\sqrt{244}\]
right?

Answer 21

Sorry, that's wrong. It's not one of the multiple choice options on my homework

Answer 22

Because that's not the answer, I only asked you if that's what you get after applying the distance formula :P

Answer 23

Nope. :P This is a homework question, it's graded on participation, can you please just fully explain the process of this problem? THANK YOU! :)

Answer 24

I'll be honest, i kind of day dremaed in class yesterday. I remember something about y-k squared... something?

Answer 25

So
\[\sqrt{244}\]
is the diameter, meaning half of that is the radius
\[\frac{\sqrt{244}}{2}\]
is the radius

Let's put that to one side for now.
With the endpoints, we can also determine the center of the circle, it is the midpoint of the endpoints. The x and y value of the midpoint is the average of the x and y values of the two endpoints:
\[(\frac{8 - 4}{2},\frac{7 - 3}{2}) = (2, 2)\]
The equation of a circle is given by
\[(x - h)^{2} + (y - k)^{2} = r^{2}\]
Where r is the radius and (h,k) are the coordinates of its circle.
Plugging in our radius and center, we get
\[(x - 2)^{2} + (y - 2)^{2} = (\frac{\sqrt{244}}{2})^{2} \]
\[= (x - 2)^{2} + (y - 2)^{2} = \frac{244}{4} = 61\]
so the equation is
\[(x - 2)^{2} + (y - 2)^{2} = 61\]

Answer 26

Okay, I'm going to do another one! Can you stay by me and tell if I did it properly?

Answer 27

I live to serve :D
LOL
go ahead

Answer 28

Thank you, give me a minute. The end points for this are (7,-4) (1,-10) btw

Answer 29

Wait... I've gotten to the square root of 160, but I'm stuck after that

Answer 30

Distance between the two endpoints is
\[\sqrt{(-10+4)^{2}+(1-7)^{2}}\]

Answer 31

I've gotten to the square root of 85, but now I'm stuck!

Answer 32

You still get
\[\sqrt{160}\]
?

Answer 33

....... I've gotten to the square of 160, but now I'm stuck!

Answer 34

I don't know how you could possibly get to those square roots...
Maybe you're panicking, just relax! :D
\[\sqrt{(-10 +4)^{2} + (1-7)^{2}} = \sqrt{(-6)^{2} + (-6)^{2}} = \sqrt{72} = 6\sqrt{2}\]

Answer 35

So now we have our diameter, to get the radius, just divide it by 2 :)

Answer 36

3 square root of 2

Answer 37

Yes, so we put that one side, for now, and try to figure out the center of the circle...can you do it? :)

Answer 38

no

Answer 39

The center of the circle is the midpoint of the given endpoints
(Makes sense, right? The center of the circle would surely be the center of the diameter as well :D )

Answer 40

So now can you do it?

Answer 41

no

Answer 42

The x-coordinate of the midpoint is the average of the x-coordinates of the endpoints
so the x coordinate is
\[\frac{1+7}{2} = 4\]
They y coordinate of the midpoint is the average of the y-coordinates of the endpoints, so can you do the y-coordinate? :)