Tangent to a Circle

RickyOswaldIOW · 2006-03-14 02:35:23

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?

RickyOswaldIOW · 2006-03-14 02:39:51

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.

Ikcelaks · 2006-03-14 05:56:43

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).

RickyOswaldIOW · 2006-03-15 09:39:05

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

Of course

RickyOswaldIOW · 2006-03-15 09:48:17

edit:

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

Math Is Fun Forum

#1 2006-03-14 02:35:23

Tangent to a Circle

#2 2006-03-14 02:39:51

Re: Tangent to a Circle

#3 2006-03-14 05:56:43

Re: Tangent to a Circle

#4 2006-03-15 09:39:05

Re: Tangent to a Circle

#5 2006-03-15 09:48:17

Re: Tangent to a Circle

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