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Calculus, derivatives in action

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data

    I made a thread last week where I had a reasonable idea what was going on in 2 problems last week
    this week I have 2 problems where i have NO idea where to start.

    Show that the ellipse x2 +2 y2 =2 and the hyperbola 2 x2 -
    2 y2 =1 intersect at right angles.

    What is the first time after 3 o'clock that the hands of the clock are together?
    2. Relevant equations

    3. The attempt at a solution

    1st problem, all I know is that perpendicular lines have similar slopes( dunno how to explain , for example 1 line has slope of 4 , perpendicular has to have a slope of -1/4).

    but why does that matter? these are not lines so slopes shouldnt even matter at all, should I use implicit differentiation? even if I do, what for?

    2nd problem, dunno how to start, cant even draw a diagram , t.t help!
  2. jcsd
  3. Oct 27, 2011 #2


    User Avatar
    Science Advisor

    Well, you posted this in the "Calculus and Beyond" section so you must know of "tangent" lines and derivatives. Two curves are perpendicular at a point of intersection if and only the tangent lines at those points are perpendicular.

    For (2), have you drawn a picture? You know the hour hand must lie between "3" and "4" on the clock face. For the minute hand to be in the same position, the time must be between 3:15 and 3:20. Can you narrow that down?
  4. Oct 27, 2011 #3


    Staff: Mentor

    Your example is correct, but the lead-in text isn't. Perpendicular lines have slopes that are negative reciprocals of each other.
  5. Oct 27, 2011 #4

    This helped a LOT, here's what I did:

    Differentiate implicitly two functions, here's what I got

    dy1/dx= -x/2y


    So since slopes must be perpendicular

    -x/2y * x/y=-1
    This is where I got stuck for a long time, here's what I did next

    x2 +2 y2=2
    2x2-2y2=1 multiply by 2

    4x2 -2y2=2 =>

    x2 +2 y2=4x2 -2y2

    but hey! thats what we got before!

    doing second one
  6. Oct 28, 2011 #5
    well yea obviously, since the hour arrow cant be more than half(3.175) because the minute one has to be in same range, so its somewhere 3.16-3.17 ish, but how exactly does that relate to calculus?rate of change of arrows?

    obviously the minute arrow changes faster, but how much faster is question for me, i dunno how to relate this to derivatives.
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