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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

I need to find the equations of tangents on circles at certain points.

I have the co-ords of the point(p) and the co-ords of the center(c). To work out the gradient of the radius from the center to the point I do:

y(c) - y(p) / x(c) - x(p)

Is this correct or should I take (p) - (c) instead?

Aloha Nui means Goodbye.

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

x² + y² = 8 at (2, 2)

(2)² + (2)² - 8 = 0 (satisfy that the point lies on the circle)

x² + y² = 8

(x + 0)² + (y + 0)² = 8

center point is (0, 0).

0 - 2/0 - 2 = -2 / -2 = 1

the gradient of the radius is 1 and thus the gradient of the tangent is -1.

y - 2 = -1(x - 2) --> y = x + 4.

Aloha Nui means Goodbye.

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**Ikcelaks****Member**- Registered: 2006-03-13
- Posts: 8

Your equation for the gradient of the radius is correct. Note that it doesn't matter if you take p - c or c - p as long as you are consistent (sign switches in both numerator and denominator and thus cancels).

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

Note that it doesn't matter if you take p - c or c - p

Of course

Aloha Nui means Goodbye.

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**RickyOswaldIOW****Member**- Registered: 2005-11-18
- Posts: 212

edit:

y - 2 = -1(x - 2) --> y = **-**x + 4.

Aloha Nui means Goodbye.

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