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Equation Tangent to curve

  1. Oct 16, 2007 #1
    Find the equation of the line tangent to the curve at (5, -3)
    (x-2)^2 + (y+3)^2 = 9

    I solved the derivative to be dy/dx = ((-2x+4)/ (2y+6))

    when i plugged in the points (5, -3) I got the slope as -6/0...How is this possible??
    How can i find the equation of this curve if the slope is undefined??
  2. jcsd
  3. Oct 16, 2007 #2


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    If the gradient is undefined then, the tangent is vertical line e.g.x=1

    btw: that curve, represents a circle with radius 3 and centre (2,-3) so if you are still confused about it, just make a sketch and see
    Last edited: Oct 16, 2007
  4. Oct 16, 2007 #3
    wait if its a circle then why isnt the equation x = 5?
  5. Oct 16, 2007 #4


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    The equation is x=5, I just used x=1 as an example of what the equation of a line with an undefined gradient looks like
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