The shortest distance between the p...
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The shortest distance between the parabolas 2y2 = 2x – 1, 2x2 = 2y – 1 is (2) 2012 (6) (0) 4 (2) B (b) 212 23

JEE/Engineering Exams
Maths
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[ 2 y^{2}=2 x-1 ] Dibterentiation gives. [ begin{array}{c} 4 y frac{d y}{d x}=2 x d y end{array} quad begin{array}{r} 4 x=2^{d y} frac{d x}{d x} frac{d y}{d x}=2 x=1 end{array} ] ( frac{d y}{d x}=frac{1}{2 y}=1 ) ( therefore x=1 / 2 ) ( y=1 / 2 ) and ( y=34 ) and ( x=314 ) The destance buo thin Miuts gives distance tha shostest [ begin{aligned} d &=sqrt{left(frac{1}{2}-frac{3}{4}right)^{2}+left(frac{3}{4}-frac{1}{2}right)^{2}} &=sqrt{frac{1}{16}+frac{1}{16}}=sqrt{frac{2}{frac{2}{82}}}=frac{1}{2 sqrt{2}} end{aligned} ]
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