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The locus of the vertices of the family of parabolas `y =[a^3x^2]/3 + [a^2x]/2 -2a` is:A. `xy=(105)/(64)`B. `xy=3/4`C. `xy=35/16`D. `xy=64/105` |
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Answer» Correct Answer - A We know that the vertex of the parabola given by `y=ax^(2)+bx+c` is at `((-b)/(2a),(-D)/(4a))`, So the coordinates of the verteds of the parabola `y=a^(3)/3x^(2)+a^(2)/2x-2a," are "((-3)/(4a),(-35a)/(16))` Thus, if (h, k) are the coordinates of the vertex. Then, `h=(-3)/(4a)" and K"=(-35a)/(16)rArrhk=(105)/(64)` Hence, the locus of (h, k) is `xy=(105)/(64)`. |
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