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From a point (sintheta,costheta), if thr...

From a point `(sintheta,costheta)`, if three normals can be drawn to the parabola `y^(2)=4ax` then the value of a is

A

A. `(1/2,1)`

B

B. `[-1/2,0)`

C

C. `[1/2,1]`

D

D. `(-1/2,0)cup(0,1/2)`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) Point `(sintheta,costheta)` lies on the circle `x^(2)+y^(2)=1" for "AAthetainR`.
Now, three normals can be drawn to the parabola `y^(2)=4ax` if `x=|2a|` meets this circle.
Hence, we must have
`costhetagt|2a|`
`or0lt|2a|lt1`
`or0|a|lt(1)/(2)`
`orain(-(1)/(2),0)cup(0,(1)/(2))`
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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  2. If the normals to the parabola y^2=4a x at three points (a p^2,2a p), ...

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  3. Normals A O ,A A1a n dA A2 are drawn to the parabola y^2=8x from the p...

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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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  5. From a point (sintheta,costheta), if three normals can be drawn to the...

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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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