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In the xy plane three distinct lines l1,...

In the xy plane three distinct lines `l_1,l_2,l_3` are concurrent at `M(lambda,0)`. Also the lines `l_1,l_2,l_3` are normals to the parabola `y^2 =6x` at the points `A(x_1,y_1), B(x_2,y_2) ,C(x_3,y_3)` respectively. Then

A

`lambda lt -5`

B

`lambda gt 3`

C

`-5 lt lambda lt -3`

D

`0 lt lambda lt 3`

Text Solution

Verified by Experts

The correct Answer is:
B
Any normal
`y=mx-2am-am^(3)` Here `a=3//2`
through `(lambda, 0)`
`0= m lambda-2 am-am^(3)`
`m=0, lambda=2a+am^(2)`
`m^(2)=lambda/a-2 gt 0`
`lambda gt 2a rArr lambda gt 3`
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