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Let N be the foot of perpendicular to th...

Let `N` be the foot of perpendicular to the x-axis from point `P` on the parabola `y^2=4a xdot` A straight line is drawn parallel to the axis which bisects `P N` and cuts the curve at `Q ;` if `N O` meets the tangent at the vertex at a point then prove that `A T=2/3P Ndot`

A

`3//2`

B

`2//3`

C

1

D

none

Text Solution

Verified by Experts

The correct Answer is:
B
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MOTION-PARABOLA-EXERCISE - I
  1. If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then ...

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  2. let P be the point (1, 0) and Q be a point on the locus y^2= 8x. The l...

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  3. Let N be the foot of perpendicular to the x-axis from point P on the p...

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  4. The locus of the midpoint of the segment joining the focus to a moving...

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  5. If (t^2, 2t) is one end ofa focal chord of the parabola, y^2=4x then ...

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  6. Find the locus of the point of intersection of the perpendicular ta...

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  7. Find the common tangent of x^(2) + y^(2) = 2a^(2) and y^(2) = 8ax.

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  8. The tangents to the parabola x = y^2 + c from origin are perpendicular...

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  9. T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respect...

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  10. P Q is a normal chord of the parabola y^2=4a x at P ,A being the verte...

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  11. The normal at the point (bt1^2, 2bt1) on the parabola y^2 = 4bx meets ...

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  12. Locus of the intersection of the tangents at the ends of the normal ch...

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  13. If the normal chhord of the parabola y^(2)=4x makes an angle 45^(@) wi...

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

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  15. Tangents are drawn from the points on the line x-y+3=0 parabola y^2=8x...

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  16. The line 4x-7y + 10 = 0 intersects the parabola, y^2 = 4x at the point...

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  17. From the point (4, 6) a pair of tangent lines are drawn to the parabol...

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  18. PSQ is a focal chord of the parabola y^2=8xdotIf\ S P=6, then write SQ...

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  19. The equation of the circle drawn with the focus of the parabola (x – 1...

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  20. The slope of the focal chords of the parabola y^(2) = 16x which are ta...

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