Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Determining Tangent Slope w/Point Not On Curve

  1. Apr 25, 2012 #1
    How do you determine the equation of all possible tangents to a curve (say, a parabola) that pass through a given point that is not on said curve? This is more of a conceptual question, and it's not homework, so I thought it fit in this forum. I think there might be a question like this on the test tomorrow. :wink:
  2. jcsd
  3. Apr 26, 2012 #2
    You write down the line equation as l(x, t) = (x, f(x)) + t(1, f'(x)) and solve a system of equations l(x, t) = p, where p is the point you want to pass. You then have all values of x that have a tangent you want.
    If the curve is given implicitly instead, as F(x, y) = 0, you can find a normal n(x, y) = (dF(x, y)/dx, dF(x, y)/dy). Then you write an implicit line equation <n(x, y), p> = <n(x, y), (x, y)> and get another implicit curve. Lastly, you need to find where this curve intersects with the given curve.
    I'm not sure this is the easiest way though.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook