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tango2009 asked on

Circle intersection

I am trying to find out if these two circles intersect with eachother

(x-2)2 +(y+2)2 = 1

how do I do this?
Math / Science

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nickalh

8/22/2022 - Mon
d-glitch

That's only one circle.
d-glitch

The way to check if two circles intersect is to look at the distance between their centers
and the sum of their radii.
d-glitch

Do you know how to find the center and radius of this circle:

        (x-2)² +(y+2)² = 1
Your help has saved me hundreds of hours of internet surfing.
fblack61
phoffric

This has nice pictures to help visualize:
      http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/

It not only addresses your question, but also identifies the points of intersection.

There is even a link at the top that has a C source code example by Tim Voght.
ASKER
tango2009

sorry made a mistake in posting its these two circles

(x-2)2 +(y+2)2 = 1
x2 +y2 = 4

thanks for your reply phroffic I will have a go using your link
phoffric

The previous link was for good pictures and some c-code.
Here is a math link that starts off with the basic equations.
     http://www.sonoma.edu/users/w/wilsonst/papers/geometry/circles/default.html

BTW - some notation for writing on EE to show raising to the power of 2:
(x-2)^2 +(y+2)^2 = 1
x^2 +y^2 = 4

You can even do:
(x-2)² +(y+2)² = 1
x² +y² = 4
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ASKER
tango2009

This is how far Iv got can you see if I am doing this right

(x-2) ^2 + (y+2)^2 = 1
x^2 + y^2 = 4

(x + 2 + y + 2 -1) + (x^2 + y^2 - 4)

x + y + 4x + 4y

x + y -8

= 4 (x + y -2 )

Y = (-4x + 8) / 4 = -x + 2 -> 2 - x

next I have to substitute the value of y in the eqaution. I am on the right tracks so far or am I off point.
ozo

What do those lines represent?
What's on the left of the 3rd = ?
Do you need to find the points of intersection, or just determine whether they intersect?
ASKER
tango2009

These are two circles that I have to check if they intersect or not?

'What's on the left of the 3rd = ?' Not sure which one you mean. Is it this bit =4 ( x + y - 2) if so thats a typo sorry there shouldn't be an eqauls there.
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ozo

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phoffric

In my previous link is this link:
     http://www.sonoma.edu/users/w/wilsonst/papers/geometry/circles/T1--2/T1-3-1.html
which helps you understand the coordinates of the center of a circle and the radius.
ASKER
tango2009

Ok

So with this eqaution (x-2)² +(y+2)² = 1

The centre of the circle is (2,2) and the radius is 1

With the other equation isn't the radius 4 and the centre (2,2)?
phoffric

>> the radius is 1
Yes

>> The centre of the circle is (2,2)
No. Take a look at the formulas and be careful about the signs.

Hint:  You probably know this:    +9 = -(-9)
But see if you can apply this idea to the center of circle problem.
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phoffric

>> x^2 + y^2 = 4
>> isn't the radius 4 and the centre (2,2)?

Ok, you are saying that r = 4, x0 = y0 = 2.
Test out your idea by plugging in your values into the circle equation from the link:

(x - x0)² + (y - y0)² = r²

Write down the equation plugging in the values. The equation you come up with will be a circle whose center is (2,2) and whose radius is 4. Does this equation match the equation of the one you posted?
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phoffric

correction to cut and paste error:By inspection, you can see that x0 is -19, y0 is 17, and r is 6; so we have a circle whose center is   (-19, 17) and whose radius is 6.
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