Let L be a common tangent line to the curves
4x2 + 9y2 = 36 and (2x)2 + (2y)2 = 31. Then the
square of the slope of the line L is __________.
Answer (integer)
3
Solution
Tangent to the curve ${{{x^2}} \over 9} + {{{y^2}} \over {14}} = 1$ is <br><br>$y = mx + \sqrt {9{m^2} + 4}$<br><br>and equation of tangent to the curve ${x^2} + {y^2} = {{31} \over 4}$ is<br><br>$y = mx + \sqrt {{{31} \over 4}{{(1 + m)}^2}}$<br><br>for common tangent $9{m^2} + 4 = {{31} \over 4} + {{31} \over 4}{m^2}$<br><br>$\Rightarrow {5 \over 4}{m^2} = {{15} \over 4}$<br><br>$\Rightarrow {m^2} = 3$
About this question
Subject: Mathematics · Chapter: Conic Sections · Topic: Parabola
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