If two different tangents of `y^2=4x` are the normals to `x^2=4b y ,` then `|b|>1/(2sqrt(2))` (b) `|b|<1/(2sqrt(2))` `|b|>1/(sqrt(2))` (d) `|b|<1/(sqrt(2))`

Options

A. `|b|gt1//2sqrt(2)`
B. `|b|lt1//2sqrt(2)`
C. `|b|lt1//sqrt(2)`
D. `|b|lt1//sqrt(2)`

Answer

B

Explanation

(2) Tangent to `y^(2)=4x` in terms of m is
`y=mx+(1)/(m)` (1)
Normal to `x^(2)=4by` in terms of m is
`y=mx+2b+(b)/(m^(2))` (2)
Equation (1) and (2) represent same line, then
`(1)/(m)=2b+(b)/(m^(2))`
`or2bm^(2)-m+b=0`
For two different tangents
`1-8b^(2)gt0`
`or|b|lt(1)/(sqrt(8))`