# Thread: points of intersection quiz

1. ## 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..

2. ## 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. (:

3. ## 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