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The value of thetain(-pi/2, pi/2) for wh...

The value of `thetain(-pi/2, pi/2)` for which the line `y=x" cos "theta+4" cos" ^(3)" "theta-14" cos "theta-1` is a normal to the parabola `y^(2)=16x,` is

A

`pi//3`

B

`pi//6`

C

`pi//9`

D

`pi//4`

Text Solution

Verified by Experts

The correct Answer is:
C
The slope of the given line is m = cos `theta`.
We know that the line y = mx + c is a normal to the parabola `y^(2)=4ax`, if `c=-2am-am^(3)`. Therefore, the given line will be a normal to the parabola `y^(2)=16x,` is
`4 cos^(3)theta-14costheta-1=-8costheta-4cos^(2)theta`
`rArr" "8cos^(3)theta-6costheta=1`
`rArr" "2(4cos^(3)theta-3costheta)=1`
`rArr" "2cos3theta=1rArrcos3theta=1/2rArr3theta=pi/3theta=pi/9`
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Chapter Test
  1. The value of thetain(-pi/2, pi/2) for which the line y=x" cos "theta+4...

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  2. If y=2x+k is a tangent to the curve x^(2)=4y, then k is equal to

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  3. The normal drawn at a point (a t1 2,-2a t1) of the parabola y^2=4a x m...

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  4. The mid-point of the chord 2x+y-4=0 of the parabola y^(2)=4x is

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  5. The two ends of latusrectum of a parabola are the points (3, 6) and (-...

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  6. Prove that the locus of the middle points of all chords of the parabol...

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  7. The focus of the parabola x^2-8x+2y+7=0 is

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  8. The point of contact of the line x-2y-1=0 with the parabola y^(2)=2(x-...

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  9. Find the number of distinct normals that can be drawn from (-2,1) to t...

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  10. At what point on the parabola y^2=4x the normal makes equal angle with...

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  11. Three normals to the parabola y^2= x are drawn through a point (C, O) ...

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  12. The normal chord of a parabola y^2= 4ax at the point P(x1, x1) subten...

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  13. AB, AC are tangents to a parabola y^2=4ax; p1, p2, p3 are the lengths...

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  14. The circles on the focal radii of a parabola as diameter touch: A) th...

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

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  16. about to only mathematics

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  17. The equation of the tangent to the parabola y^(2)=8x which is perpendi...

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  18. the tangent drawn at any point P to the parabola y^2= 4ax meets the di...

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  19. about to only mathematics

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  20. The parabola y^(2)=4ax passes through the point (2,-6). Find the lengt...

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  21. A variable circle passes through the fixed point (2, 0) and touches y-...

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