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Normals A O ,AA1a n dAA2 are drawn to th...

Normals `A O ,AA_1a n dAA_2` are drawn to the parabola `y^2=8x` from the point `A(h ,0)` . If triangle `O A_1A_2` is equilateral then the possible value of `h` is 26 (b) 24 (c) 28 (d) none of these

A

26

B

24

C

28

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
(3) Let `A_(1)-=(2at_(1)^(2),4t_(1))andA_(2)-=(2t_(1)^(2),-4t_(1))`.
Clearly, `angleA_(1)OA=pi//6`. Therefore,
`(2)/(t_(1))=(1)/(sqrt(3))`
The equation of normal of normal at `A_(1)` is
`y=-t_(1)x+4t_(1)+2t_(1)^(3)`
`orh=4+2t_(1)^(2)=4+2(12)`
=28
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