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Math Help - points of intersection quiz

  1. #1
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    points of intersection quiz

    I have been looking for points of intersection problems but I can't find many good ones. Can anyone here make a points of intersection quiz? I'm talking about not just lines but all the way up to nonlinear equations, conics and trigonometric/transcendental functions.. Very hard to find a good quiz on this for practicing..
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  2. #2
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    Re: points of intersection quiz

    For the following problems find solutions if they exist:

    Problem 1: There are two circles and an ellipse. Their equations respectively are: \text{Eqn1:}\quad x^2+y^2=a^2 ,  \text{Eqn2:}\quad (x-h)^2+(y-k)^2 = b^2, and  \frac{(x-a)^2}{h^2}+\frac{(y-b)^2}{k^2}=1 Find all points of intersections along the three curves in terms of a, b, h, and  k . Assume b>k>a>h

    Problem 2: Find the point(s) of intersection of  y_1= x^5-x^3+5 and  y_2=-x^4-4x^2+3 .

    Problem 3: Find the point(s) of intersection of  y_1 = e^{\sin^2(x)}e^{cos^2(x)} and  y_2=ln|x| find all points of intersection of the curves.

    Problem 4: Find the point(s) of intersection  y_1 = \frac{1}{e^{x}+1} and  y_2 = e^{-x}

    if you can do these you should be able to handle most intersection problems. I threw problem 1 in there for a real challenge and I made up all of these on the fly. Let me know how they go and if I can help you. (:
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  3. #3
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    Re: points of intersection quiz

    I haven't started yet... I'm on the last week of an integral calculus class.. delay before I can start answering this is probably one week tops
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