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Normals A O ,A A1a n dA A2 are drawn to ...

Normals `A O ,A A_1a n dA A_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

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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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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  4. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

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  6. If the normals at P(t(1))andQ(t(2)) on the parabola meet on the same p...

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  7. If the normals to the parabola y^2=4a x at P meets the curve again at ...

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  8. PQ is a normal chord of the parabola y^2 =4ax at P, A being t...

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  9. P ,Q , and R are the feet of the normals drawn to a parabola (y-3)^2=8...

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  10. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

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  11. The endpoints of two normal chords of a parabola are concyclic. Then ...

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  12. If normal at point P on the parabola y^2=4a x ,(a >0), meets it again ...

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  13. The set of points on the axis of the parabola (x-1)^(2)=8(y+2) from wh...

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  14. Tangent and normal are drawn at the point P-=(16 ,16) of the parabola ...

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  15. In parabola y^2=4x, From the point (15,12), three normals are drawn th...

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  16. The line x-y=1 intersects the parabola y^2=4x at A and B . Normals at ...

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  17. If normal are drawn from a point P(h , k) to the parabola y^2=4a x , t...

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  18. The circle x^(2)+y^(2)+2lamdax=0,lamdainR, touches the parabola y^(2)=...

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  19. The radius of the circle whose centre is (-4,0) and which cuts the par...

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  20. If normal at point P on the parabola y^2=4a x ,(a >0), meets it again ...

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