Question

What is special about the standard equation of a circle? Help please I have no idea!

Answer 1

you have very weird subjective question hmm I think you can find the center and radius directly from the standard

Answer 2

I don't know I am not sure but this my guess...and something I find special with circle eq lol

Answer 3

I don't either. My teacher asked it and I can't move on without knowing it but I'm very confused.

Equation of a circle where (h, k) is the center and r is the radius: (x − h)2 + (y − k)2 =r2 The formula for a circle (x − h)2 + (y − k)2 = r2 can also be re-arranged and written as:
x minus h quantity squared all over r squared + y minus k quantity squared all over r squared = 1

so i guess you're right about finding the center and the radius. But how would I explain how you do that?

Answer 4

sorry I am not sure what your question is but lets take an example (x-5)^2+(y+3)^2 = 16
can you find center and radius of this circle?

Answer 5

No I have no idea :( Do I just solve that equation?

Answer 6

so if you look closely you can see value of (h,k) and r
hint (x-5)^2+(y-(-3))^2=(4)^2

Answer 7

I have no idea I'm sorry

Answer 8

k so say I ask you to write a equation of circle with radius 4 and center (5,-3) can you do that?

Answer 9

So...would it be....(x-5)^2+(y+3)^2=16?

Answer 10

WAIT that's what you just posted!

Answer 11

Great! so can you tell me the center and radius for circle by just looking at the equation?
you just have to figure out value of (h,k) and r

Answer 12

so the center would be (-5,3) and r would be 16?

Answer 13

Noooooooooooooooo

Answer 14

Does it change after you make it an equation? Cause you said before it was (5,-3) and 4

Answer 15

But in the equation it looks like (-5,3) and 16

Answer 16

just check the radius again and also tell me for this new one (x-2)^2+(y+8)=36

Answer 17

would it be...(2,-8) and 6?

Answer 18

Yes I think you got the concept! good job :)

Answer 19

Thank you!

Answer 20

np :)

Answer 21

And please do let me know what you teacher thinks is special in circle equation

Answer 22

I guess I could say for my actual question lol is that you can find the center and the radius and that the equation is derived from Pythagorean Theorem. Not sure if it'll be right but I'll let you know lol

Answer 23

idk if it helps you can add that point x and y are at a constant distance r from the center.

Answer 24

Oh I'll add that too just to see if it's right, I'll let you know what she says in a little :) thanks again!

Answer 25

np :) Yeah I would like to know the answer

Answer 26

Okay, so basically all she wanted was that (h,k) was the center and r was the radius. Then she wanted me to solve \[(x-5)^2/16+(y+5)^2/16=1\]

Answer 27

To change that into the normal circle equation and I got it right. Thank you for teaching me!!!

Answer 28

haha Ok so that was special thing about circle good to know!