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Two Lines and a Hyperbola

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February 15, 2009
conicshyperbolaAsymptoteanalytic geometrygraphing linesslope

Problem Statement

If each of two intersecting lines intersects a hyperbola and neither line is tangent to the hyperbola, then the possible number of points of intersection with the hyperbola is: <spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 2 or 3<spanclass=′latex−bold′>(C)</span> 2 or 4<spanclass=′latex−bold′>(D)</span> 3 or 4<spanclass=′latex−bold′>(E)</span> 2,3, or 4 <span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 2\text{ or }3 \qquad<span class='latex-bold'>(C)</span>\ 2\text{ or }4 \qquad<span class='latex-bold'>(D)</span>\ 3\text{ or }4 \qquad<span class='latex-bold'>(E)</span>\ 2,3,\text{ or }4
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