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# P3 circles touching each other watch

1. Could anyone help me with this question?

Show that the circles with equations x² + y² - 6x + 4y –23 = 0 and
x² + y² - 22x – 8y + 121 = 0 touch each other and find the coordinates of their common point.

Thanks! Any help would be appreciated as I have my exam tomorrow.
2. (Original post by *hedgehog*)
Could anyone help me with this question?

Show that the circles with equations x² + y² - 6x + 4y –23 = 0 and
x² + y² - 22x – 8y + 121 = 0 touch each other and find the coordinates of their common point.

Thanks! Any help would be appreciated as I have my exam tomorrow.
x² + y² - 6x + 4y –23 = x² + y² - 22x – 8y + 121
-6x+4y-23=-22x-8y+121
16x+12y=121+23, put this equation back into one of the circle equations and solve for x or y, then hence find coordinates.
3. (Original post by *hedgehog*)
Could anyone help me with this question?

Show that the circles with equations x² + y² - 6x + 4y –23 = 0 and
x² + y² - 22x – 8y + 121 = 0 touch each other and find the coordinates of their common point.

Thanks! Any help would be appreciated as I have my exam tomorrow.
x² + y² - 6x + 4y –23 = x² + y² - 22x – 8y + 121

Solve to find y in terms of x, then sub back into one of the equations and show there is only one solution.
4. cheers!

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