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If two different tangents of y^(2) = 4x ...

If two different tangents of `y^(2) = 4x` are the normals to `x^(2) = 4` by then :

A

`|b|ge(1)/(2sqrt2)`

B

`|b|lt(1)/(2sqrt2)`

C

`|b|gt(1)/(sqrt2)`

D

`|b|lt(1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Eq of any tangent to `y^(2)=4x` in terms of m is
`y=mx+(1)/(m)" ……(i)"`
Eq of any normal to `x^(2)=4by` in terms of m is
`y=mx+2b+(b)/(m^(2))" …….(ii)"`
Equation (i) and (ii) represent the same line
`therefore" "(1)/(m)=2b+(b)/(m^(2))`
`or 2bm^(2)-m+b=0`
For two distinct values of m
`D=(-1)^(2)-4(2b)(b) gt0`
`rArr 1-8b^(2)gt0`
`rArr" "b^(2)lt(1)/(8)`
`rArr" "|b|lt(1)/(2sqrt2)`
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