Question

The graph of a line and an exponential can intersect twice, once, or not at all. Describe the possible number of intersections for each of the following pairs

of graphs. Your solution to each part should include all of the possibilities and a quickly sketched example of each one.

A. A line and a parabola
B.Two different parabolas
C.A parábola and a circle
D. A parabola and the hyperbola y=1/x

Answer 1

• c) parabola and circle: 0, 1, 2, 3, 4 times

• d) parabola and hyperbola: 1, 2, 3 times

Explanation:

c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.

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d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.

If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.