Question

For the circle with equation (x – 2)^2 + (y – 1)^2 = 16
2. Answer each question.
(a) What are the coordinates of the center?

(b) What are the radius and diameter of the circle?

(c) Graph the circle.

Answer 1

@Directrix @Nnesha

Answer 2

@zepdrix

Answer 3

It's important that you know and understand how to use the general equation of a circle of radius r, centered at the point (h,k):\[(x-h)^2+(y-k)^2=r^2\]

Answer 4

Compare your particular equation to this one. What are y our h, k and r?

Answer 5

k is 1 h is 2 and y is unknown? @mathmale

Answer 6

Stop for a minute and think of what you're trying to do: Find the center and radius of a given equation of a circle. You were not asked to find x or y; you were asked to find the coordinates of the center of the circle, represented by (h,k). So, it doesn't help if you write "y is unknown."

What is h? k? r?

You were given:

(x – 2)^2 + (y – 1)^2 = 16
Please write the general equation of a circle centered at (h,k) with radius 2 below the given equation. Compare them. Find h, k and r thru this comparison.

Answer 7

(x – 2)^2 + (y – 1)^2 = 16
(x – h)2 + (y – k)2 = r2
H = 2 K = 1 idk how to find r @mathmale

Answer 8

@mathmale are you still there?

Answer 9

@zepdrix can you help me finish this? @mathmale went offline

Answer 10

Sup? Where we at? :o

Answer 11

read above

Answer 12

Im so lost this was the most confusing unit of math ever

Answer 13

\[\large\rm (x-2)^2+(y-1)^2=16\]So you've determined that the center is located at \(\large\rm (h,k)=(2,1)\).
And next we need to figure out the radius.

Answer 14

ok

Answer 15

The right side of the equation is supposed to be written as a square.
It's not very helpful when it's not written in that form.

Is there some way to rewrite 16 as a number squared?

Answer 16

4^2

Answer 17

\[\large\rm (x-2)^2+(y-1)^2=4^2\]Ooo that might help us,
that more closely resembles the general form of a circle, ya?\[\large\rm (x-h)^2+(y-k)^2=r^2\]

Answer 18

Are you able to spot the radius when it's in that form?

Answer 19

4

Answer 20

Good good good.
Understand how to get the diameter from that information?

Answer 21

im not quite sure 4 times 2 = 8, is that right?

Answer 22

yay good job!

Answer 23

ok whats next?

Answer 24

we'll use these key features that we've determined so far,
to help us graph the circle.

Answer 25

ok

Answer 26

In the upper right corner of the picture, there is a "copy picture" button.
Do you know how to use that?
Wanna try labeling the center?

Answer 27

sure i think i can do that

Answer 28

is that correct?