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Find m^2

Source: 1971 AHSME Problem 19

April 20, 2014
conicsellipsequadraticsalgebraquadratic formulaAMC

Problem Statement

If the line y=mx+1y=mx+1 intersects the ellipse x2+4y2=1x^2+4y^2=1 exactly once, then the value of m2m^2 is
<spanclass=′latex−bold′>(A)</span>12<spanclass=′latex−bold′>(B)</span>23<spanclass=′latex−bold′>(C)</span>34<spanclass=′latex−bold′>(D)</span>45<spanclass=′latex−bold′>(E)</span>56<span class='latex-bold'>(A) </span>\textstyle\frac{1}{2}\qquad<span class='latex-bold'>(B) </span>\frac{2}{3}\qquad<span class='latex-bold'>(C) </span>\frac{3}{4}\qquad<span class='latex-bold'>(D) </span>\frac{4}{5}\qquad <span class='latex-bold'>(E) </span>\frac{5}{6}
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