Question

Trig Question

The equation for a circle not at the origin is
(x-H)^2 + (y-K)^2 = R^2

H and K being the center coordinates and the R^2 is the radius

The book then gives the example of
point ( 3, -2) for the center and says the equation would now look like this

(x-3)^2 + (y+2)^2 = 81

Why are the signs reveresd all of a sudden? I do not understand?
It says that the point are 3,-2

So why all of a sudden in the equation is it -3 and +2???

Answer 1

the definition of circle is that a circle is a locus of such points that keep a specific distance from a particular point and the particular point is centre and the distance is radius. let the centre be (h,k)
sor for any point (x,y) the distance between (x,y) and (h,k) is sqrt((x-h)^2+(y-k)^2)
now if the point (x,y) is on a circle then
(x-h)^2+(y-k)^2=R^2 thus the -ve sign comes

Answer 2

( 3, -2) means x is 3, y is -2 instead of (0,0) when it would be just x^2 + y^2

(x-3)^2 + (y+2)^2 = 81 so x is 3 here and y is -2 to "bring it back" to (0,0)

Answer 3

He said informally....

Answer 4

@ estudier what you have said is not correct .in the equation of circle the x,y, is the moving point not the center socan't say x=3,x=-2 .

Answer 5

Ease up, I said informally, it works for me (every time).

Answer 6

but the actual thing always comes fromthe definition

Answer 7

I wasn't saying u were wrong.....

Answer 8

I still dont get this, all i have gathered so far is that is that you need to reverese the singes. I get that we are adding or subtracting a certain # of unties from the origin to place the center at a different location but i dunno why the signs would change

Answer 9

If you think of it in (x,y) terms then they haven't.....

Answer 10

Are u translating the plane or the circle? Either?

Answer 11

Try it with a line.

Do it with y¨= x and translate it up and own, etc.

Answer 12

Im not translating any thing, my book just says here is point 3,-2 and radius 9 plug it into the equation. and then it gives the answer (x-3) + (y+2) and i have no clue why the signs are revered with no explination in the book whatsoever

Answer 13

Here's a picture, have a look and tell me what u think....

(remember, these are plotted points,even if its a computer doing it).

Answer 14

http://www.wolframalpha.com/input/?i=plot+x^2%2By^2+%3D1%2C+%28x-3%29^2+%2B%28y-2%29^2+%3D1

Answer 15

Not to but in but, isn't it simply because two negatives = a positive??

Answer 16

The thing is with this sort of thing, each has to get his won intuition of what's going on.

Somepeople like a geometric explanation, others algebraic and so on...

Answer 17

(x-3)^2 + (y-(-2))^2 = 81

Answer 18

Oh ok, yea.. I understand the delema. ha ha

Answer 19

Basically, your way and my way are the same, sort of...

Answer 20

@bassk

do u see it better now....?

Answer 21

well i see the grapgh im kinda starting to get it but what does a - and a - making a postive have to do with anything?

Answer 22

That's that person's way of getting to grips with what a translation means....

Answer 23

Each to his own, play around in Wolfram with different graphs and picture or do some algebra until u come up with something that is satisfying to u personally..

Answer 24

You know what is supposed to be (the answer), u just need to be able to explain it(to yourself).

Answer 25

Well in looking at the graph we have x-3 and we are sayinbg that previosuld x= 0 the the new point would be -3 but the its a positve 3 on the grapgh this is driving me nuts

Answer 26

Imagine that the circle did not move, the plane "behind" it (including the x and y axes moved instead, does that help?

Answer 27

I see what your saying, in the the circle not moving but the grapgh u sent me has the origin at +3 right so how can x be = 0 and we say 0-3 = +3

Answer 28

also we are saying (0-3) ^2 so how is that not -9

Answer 29

I'm not quite sure I understand u.

Anyhow, now u got the idea I think, imagine the plane moving backwards and forwards, and think about how the equation must change to accommodate that.