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 Calculus Calculus Math Forum

 February 3rd, 2013, 09:47 PM #1 Member   Joined: Jan 2013 Posts: 54 Thanks: 0 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? 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. Tags intersection, points point of intersection f o g equation

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