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A B is a chord of the parabola y^2=4a x ...

`A B` is a chord of the parabola `y^2=4a x` with vertex `AdotB C` is drawn perpendicular to `A B` meeting the axis at `Cdot` The projection of `B C` on the axis of the parabola is `a` (b) `2a` (c) `4a` (d) `8a`

A

a

B

2a

C

4a

D

8a

Text Solution

Verified by Experts

The correct Answer is:
C
In `DeltaAbD`, we have
`tantheta=y/x" ....(i)"`
`"In "DeltaBCD," we have"`
`tan(90-theta)=y/(CD)`
`rArr" CD=y tan tan "theta=y^(2)/x" "["Using (i)"]`

`rArr" "CD-=(4ax)/x=4a" "[becausey^(2)=4ax]`
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Section I - Solved Mcqs
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  2. Find the range of values of lamda for which the point (lamda,-1) is ex...

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  3. A B is a chord of the parabola y^2=4a x with vertex AdotB C is drawn p...

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  4. The coordinates of an end-point of the latusrectum of the parabola (y-...

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  5. M is the foot of the perpendicular from a point P on a parabola y^2=4a...

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  6. The equation of the parabola, whose vertex and focus are on the x-axis...

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

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  8. The point on y^(2)=4ax nearest to the focus has to abscissa equal to

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  9. The focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the eq...

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  10. Number of common chords of a parabola & a circle can be

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  11. A ray of light moving parallel to the x-axis gets reflected from parab...

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  12. If y + b = m(1)(x + a) and y + b = m(2)(x+a) are two tangents to the p...

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  13. If normals at the ends of the double ordinate x = 4 of parabola y^(2)=...

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  14. Radius of the largest circle which passes through the focus of the par...

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  15. If the tangents and normals at the extremities of a focal chord of a ...

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  16. The axis of a parabola is along the line y = x and its vertex and focu...

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  17. If the normals from any point on the parabola x^2=4y cut the line y = ...

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  18. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  19. Minimum distance between the parabola y^2-4x-8y+40=0" and "x^2-8x-4y+4...

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  20. ABCD is a square with side AB = 2. A point P moves such that its dista...

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