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