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?

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

how do I do this?

Math / Science

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.

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

(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.

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.

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

(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

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

Get an unlimited membership to EE for less than $4 a week.

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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.

(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?

What's on the left of the 3rd = ?

Do you need to find the points of intersection, or just determine whether they intersect?

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.

'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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William Peck

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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.

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.

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)?

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.

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?

>> 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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