Question

Write the standard equation of a circle with each given radius and center.
r = 4; C= (0, 0)
How do you do this?

Answer 1

Hi Shantia,
First, the equation of a circle is (x-h)^2 + (y-k)^2 = r^2

Answer 2

(h,k) is known as the center, as it is the vertical and horizontal shift.

Answer 3

Standard equation of a circle with center (a, b) and radius r is:

(x-a)²+(y-b)²=r².

Here, you have (a, b)=(0, 0) and r = 4.

Answer 4

here the center is (0,0), thus h =0 and k=0. R = 4.

Thus your equation is (x-0)^2+ (y-0)^2 = 4^2

Answer 5

Thanks guys!

Answer 6

@Mathexpert: Good explaining, but it is better to leave something do do for the asker...

Answer 7

No problem. Good luck.

Answer 8

Do I do the same for this one "r = 1; C = (2, 3)" or is it different because they are not zeros?

Answer 9

Now, (a, b) = (2, 3), so set a=2 and b=3 (and r=1) in the general equation!

Answer 10

ok

Answer 11

What equation do you get?

Answer 12

(x-2)^2+(y-3)^2=1 ???

Answer 13

Well done! You're getting it!

Answer 14

Write the standard equation for the circle given the following equations.
x2 + y2 - 8x + 7 = 0 im stuck again

Answer 15

Complete the square:

x² + y² - 8x + 7 = 0
x² - 8x + y² +7 = 0
(x-4)² - 16 + y² +7 = 0
(x-4)² + y² = 9

Answer 16

I'm lost what happened to the seven and the sixteen?

Answer 17

-16+7=-9.

That is on the left of the equal sign.
So add 9 to both sides to get ... = 9

Answer 18

ahhhhh ok I see now thanks

Answer 19

YW!

Answer 20

x2 + y2 + 4x - 6y - 3 = 0

so would this be my answer
(x-2)2 + (y-3)2 = 3

Answer 21

(x-2^)2 + (y-3)^2 = 3

Answer 22

OK, let me check:

x² + y² + 4x - 6y - 3 = 0
x² + 4x + y² - 6y - 3 = 0
(x + 2)² - 4 + (y - 3)² - 9 -3 = 0
(x + 2)² + (y - 3)² - 4 - 9 -3 = 0
(x + 2)² + (y - 3)² - 16 = 0
(x + 2)² + (y - 3)² = 16

You have to complete the squares and then take all the constan terms together and put them on the other side of the equal sign.

Answer 23

If you look well, you can see I replace:

x² + 4x with (x + 2)² - 4 and
y² - 6y with (y - 3)² - 9.

This is because (x + 2)² = x² +4x + 4, and we only need the first two terms, not the "+4". So we have to subtract 4.