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If x + by + c = 0 is normal to parabola ...

If `x + by + c = 0` is normal to parabola `y^(2) = 12x`, then complete set of all values of c is -

A

`(-oo, -6)`

B

`(9, oo)`

C

`(-oo, -6) uu (9, oo)`

D

`(-oo, oo)-{0}`

Text Solution

Verified by Experts

The correct Answer is:
A
If `y = mx +c` is normal to parabola `y^(2) = 4ax`
the `c = -2am -am^(3)`
`implies -(c/b) = -2(3)(-1/b)-(3)(-1/b)^(3)`
`implies -c/b=6/b+3/(b^3) implies (6+c) b^(2)+3=0`
`implies b^(2) = (-3)/(6+c) gt 0`
It is possible when `6+c lt 0 implies c lt -6`.
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