February 3rd, 2013, 09:47 PM  #1 
Member Joined: Jan 2013 Posts: 54 Thanks: 0  Intersection points
(x1)²+(y+2)²=1 ((x1)²/4)+(y2)²/9)=1 Prove that these two curves are tangent at all their intersection points. My memory is foggy on how to approach this. Do I just isolate x and y in both equations, then substitute x and y into their corresponding points in the equation to find the intersection points? 
February 4th, 2013, 05:46 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Intersection points
The first equation is a circle the second is an ellipse  they intersect at (x, y) = (1, 1). Implicitly differentiating the two given equations shows that the slope, for both the circle and the ellipse, at (1, 1) is 0, thus they are tangent where they intersect.


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