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February 3rd, 2013, 09:47 PM   #1
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Intersection points

(x-1)≤+(y+2)≤=1

((x-1)≤/4)+(y-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?
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February 4th, 2013, 05:46 AM   #2
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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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