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The normal at any point P(x1,y1) of curv...

The normal at any point `P(x_1,y_1)` of curve is a line perpendicular to tangent at the point `P(x_1,y_1)`. In case of rectangular hyperbola `xy=c^2`, the equation of normal at `(ct,(c )/(t))` is `xt^3-yt-ct^4+c=0`. The shortest distance between any two curves always along the common normal.
The shortest distance between the parabola `2y^2=2x-1,2x^2=2y-1` is:

A

`2sqrt(2)`

B

`(1)/(2sqrt(2))`

C

4

D

`sqrt((36)/(5))`

Text Solution

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The correct Answer is:
B
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