Question

A circle with center (1,5) passes through the point (10,10). What is the area of the circle rounded to the nearest square unit?

Answer 1

@satellite73

Answer 2

first solve for the radius of the circle

Answer 3

I'm not sure how.

Answer 4

wait ill draw it...

Answer 5

Thanks but I don't know how to solve this at all.

Answer 6

@mathmale

Answer 7

The radius is the hypotenuse of a triangle whose sides are 9 by 5
can you see that?
can you solve the radius from that?

Answer 8

plot the center and draw a line from the center up to the point where the circle pass through..

Answer 9

I'm really quite lost here...

Answer 10

Cubi-Cal: you wouldn't be in this course if you didn't already have at least some of the necessary background. The more you could review and share what you DO know that might apply to this problem, the better, and the more willing I would be to explain it from the point at which you feel stuck.

Answer 11

cubi cal - can you see how to calculate the radius?

Answer 12

see cubi-cal - we're here to help :-)

Answer 13

can u atleast know the pythagorean theorem @Cubi-Cal ?

Answer 14

There is a standard equation for a circle of radius r and center (h, k). Have you found and written down that equation for reference now and later?

Answer 15

I'm sorry guys, I'm really locking up here. This is one my last problems for my final assignment so I'm kind of at the point where I'm brain dead.

Yes! a^2+b^2=c^2

Answer 16

Okay cubi-cal - and c² would be the radius
the other 2 sides are the 'x' length and the 'y' height

Answer 17

Here's another viewpoint: If you have the center of a circle, EVERY point on that circle is the same distance from the center. Note the word "distance." Remember the distance formula? It's similar to your a^2 + b^2 = c^2, but must be modified if the center of the circle is not at (0,0).

Answer 18

Drawing a circle could be very helpful, because then you could immediately see the line drawn from the center (1,5) to the point on the circle (10,10).

Answer 19

Okay, hold on...

Answer 20

Is the radius 9?

Answer 21

Hold. I'd always prefer to see your work; otherwise I have to do it myself while you wait.

Answer 22

Do you actually have that drawing in front of you?

Answer 23

A very poor one, yes.

Answer 24

9 is wrong....

Answer 25

didi u try to use pythagorean theorem... the two sides are given by @wolf1728 .. which is 9 and 5

Answer 26

We're going to try to find the radius. To do that, you're going to need to subtract one y-component from the other y-component. J-D got that by subtracting 5 from 10. Make certain you know why he did that. Next, you'll need to find the horizontal distance from x=1 to x=10. What is that distance?

Answer 27

Oh dear. Um. 9?

Answer 28

9, for what? Say it explicitly: the horiz. distance between the vertical lines x=1 and x=10 is 9. Yes.

So now you have a right triangle with legs of 5 and 9, as J-D has already pointed out. Use the Pyth Thm to determine the length of the hypotenuse, which is also the radius of this circle.

Answer 29

So cubi-cal
the radius² = 9² + 5²
can you solve that?

Answer 30

Yes: 9 squared plus 5 squared results in the SQUARE of the radius. What is the radius itself?

Answer 31

You can find the radius itself if you wish. It just dawned on me that if you can find r^2 = a^2 + b^2, we can stop there. I'll explain why in a moment.

Answer 32

106?

Answer 33

For reference (please write this info down):

The equation of a circle centered at (0,0) is x^2 + y^2 = r^2.

The equation of a circle centered at (h, k) is \[(x-h)^2 + (y-k)^2 = r^2\]

Answer 34

Yes, great. The sqauare of the radius is indeed 106.

So now you ahve everything you need tow rite th e equation of this circle: the center and the square of the radius.

would you plese write this equatin now?

Answer 35

cubi-cal
106 is correct
that is thhe radius squared

Answer 36

How would I write the equation? Sorry.

Answer 37

You've got to know the "standard equation of a circle centered at (h,k) with radius r:"\[(x-h)^2 + (y-k)^2 = r^2\]
As before, r^2 = 106 and the center of the circle is given in the problem statement. Please write out the equation of this particular circle.

Answer 38

If the center of this circle is at ( , ) (you fill in the blanks), then the x-coordinate of the center, h, has the value ( ). Likewise, the y-coord. is ( )

Answer 39

Feel free to take the time necessary to go back to review what we've already discussed, above.

Answer 40

(1,5) and (10,10) and (10,-10)

Answer 41

The center of the circle is (1,5), meaning that the x-cooreinate, h, is 1.
The x-coord. k, is .... What?

Answer 42

x-coordinate (not cooreinate).

Answer 43

Given that the x-coord. of the center is x = h = 1, the general equation of the circle becomes more specific:\[(x-1)^2 + (y-k)^2 = r^2\]...Note how I have replaced that 'h' by '1'.

Answer 44

Finish writing this equation of your circle, please. k=?? r^2 = ??

Answer 45

I'm feeling a bit overwhelmed. I'm so very sorry!

Answer 46

doing fine cubi - math male is doing very well too

Answer 47

Thank you, you two are truly lifesavers!

Answer 48

k though?

Answer 49

tnx

Answer 50

I'm still REALLY unsure about it all.

Answer 51

on the phone at the moment - sorry :-(

Answer 52

No worries! I'm gonna close this one and open a new one. I have two more questions then no more geometry!

Answer 53

I might be able to hepp you - depending on the phone

Answer 54

Okay, no worries!

Answer 55

WAIT I got it!!

Answer 56

I just use distance formula!