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If x+y=k is normal to y^2=12 x , then k ...

If `x+y=k` is normal to `y^2=12 x ,` then `k` is 3 (b) 9 (c) `-9` (d) `-3`

A

3

B

9

C

-9

D

-3

Text Solution

Verified by Experts

The correct Answer is:
B
If `y = mx + c` is normal to the parabola `y^(2) = 4ax`, then `c = - 2am - am^(3)`.
From given condition, `y^(2) = 12x`
`implies y^(2) = 4.3.x`
`implies a = 3`
And `x + y = k`
`implies y = (-1) x + k`
`implies m = -1`
and `c = k = -2 (3) (-1) - 3 (-1)^(3) = 9`
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