Question 835947
<pre>
They will have to be tangent at one point and cross at two other points:

One example is the circle x²+(y-3)² = 9 and the parabola y = x²

{{{drawing(400,400,-4,4,-1,7,graph(400,400,-4,4,-1,7,x^2),circle(0,3,3))}}}


Another example is the hyperbola {{{x^2/9-y^2/9=1}}} and the ellipse {{{(x-1)^2/16+y^2/9=1}}}

{{{drawing(400,400*5/7,-7,7,-5,5,graph(400,400*5/7,-7,7,-5,5,sqrt(x^2-9)),
graph(400,400*5/7,-7,7,-5,5,-sqrt(x^2-9)),arc(-1,0,8,6)

)}}}

Now you come up with a third one! <font size=5 face="wingdings">J</font>

Edwin</pre>