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AB is a chord of the parabola y^2 = 4ax ...

AB is a chord of the parabola `y^2 = 4ax` with its vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projecton of BC on the axis of the parabola is

A

a

B

2a

C

4a

D

8a

Text Solution

Verified by Experts

The correct Answer is:
C
(3) `tantheta=(y)/(x)`
The projection of BC on the c-axis,
`LC=(y)/(tan(90^(@)-theta))=ytantheta=(y^(2))/(x)=4a`
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. C is the centre of the circle with centre (0,1) and radius unity. y=ax...

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  2. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

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  3. AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is dr...

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  4. Set of value of alpha for which the point (alpha,1) lies inside the ci...

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  5. If X is the foot of the directrix on the a parabola. PP' is a double o...

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  6. A water jet from a function reaches it maximum height of 4 m at a d...

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  7. Area of the triangle formed by the vertex, focus and one end of latusr...

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  8. The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...

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  9. Two parabola have the same focus. If their directrices are the x-axis ...

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  10. The locus of the point (sqrt(3h),sqrt(3k+2)) if it lies on the line x-...

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  11. A circle touches the x-axis and also touches the circle with centre (0...

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  12. If parabolas y^2=lambdax and 25[(x-3)^2+(y+2)^2]=(3x-4y-2)^2 are equal...

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  13. The length of the latus rectum of the parabola whose focus is a. ((u...

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  14. The graph of the curve x^2+y^2-2x y-8x-8y+32=0 falls wholly in the (a)...

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  15. The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^...

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  16. If the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then ...

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  17. A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...

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  18. The length of the chord of the parabola y^2=x which is bisected at the...

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  19. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then th...

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  20. If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpe...

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