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2 Pre Calc problems

  1. Jan 9, 2006 #1
    Use Slopes to show that A (-3,-1),B(3,3), and C(-9,8) are vertecies of a right triangle.
    Find an equation for the line tangent to the circle x^2+y^2=25 at the point (3,-4)

    Thanks if anyone could do this that would be great.
  2. jcsd
  3. Jan 9, 2006 #2
    For the second question the easiest way is to take the derivative, evaluate it at the point to find the slope and then write the equation of a line through that point with the slope you found.
  4. Jan 9, 2006 #3
    could you do that for me thanks?
  5. Jan 9, 2006 #4


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    Yes. But we won't.

    The purpose of this forum is to help you with your homework. It is not to do your homework for you.
  6. Jan 9, 2006 #5
    These can be solved very easily using basic analytic geometry. No derivation or other nasty calculus required.

    For the first one:

    The slope can be found using for example:
    k= (y2-y1)/(x2-x1)
    (x1,y1) is the left endpoints coordinates
    (x2,y2) is the right endpoints coordinates

    if k > 0 you have a rising line
    if k < 0 you have declining line

    When two lines are at right angels to each other:
    k1 * k2 = -1
    That is, the product of the slopes equals -1.

    For the second:
    The point (3,-4) is located on the circle. (Do you know why?)
    Try to find the slope from the circles centre to (3,-4) and then use the fact that the tangent line has to be at a right angle to the slope (Why?) to calculate the slope of the tangent line.

    If you know the slope and a point you should be able to calculate the equation for the line (You probably have a formula for it).
    Last edited by a moderator: Jan 9, 2006
  7. Jan 9, 2006 #6
    k= (y1-y2)/(x2-x1)is wrong
    Slope is m = (y1-y2)/(x1-x2) not as you have given.
  8. Jan 9, 2006 #7
    Typo fixed.
  9. Jan 10, 2006 #8


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    Since this is a pre-calc problem, for number 2 try this: any line through (3,-4) can be written y= m(x-3)-4. The line tangent to x2+ y2= 25 at (3,4) must intersect it only there. For what value of m does x2+ (m(x-3)-4)2= 25 have exactly one solution for x?
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