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Conic Section

Question

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The locus of the vertices of the family of parabolas $straight y space equals fraction numerator straight a cubed straight x squared over denominator 3 end fraction space plus fraction numerator straight a squared straight x over denominator 2 end fraction minus 2 straight a space is$

$xy space equals space 105 over 64$
$xy space equals space 5 over 4$
$xy space equals space 35 over 16$
$xy space equals space 64 over 105$

Solution

A.

xy space equals space 105 over 64

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