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The tangent and normal at `P(t)`, for all real positive `t`, to the parabola `y^2= 4ax` meet the axis of the parabola in `T` and `G` respectively, then the angle at which the tangent at `P` to the parabola is inclined to the tangent at `P` to the circle passing through the points `P, T `and `G` is

A

`cot^(-1)t`

B

`cot^(-1)t^(2)`

C

`tan^(-1)t`

D

`sin^(-1)(t/(sqrt(1+t^(2))))`

Text Solution

Verified by Experts

The correct Answer is:
C
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MOTION-PARABOLA-EXERCISE - II
  1. If two tangents drawn from the point (a,b) to the parabola y^2=4x be...

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  2. Find the equation of the common tangent to the curves y^2=8x and xy=-1...

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

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  4. The equation of a straight line passing through the point (3, 6) and c...

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  5. T is a point on the tangent to a parabola y^(2) = 4ax at its point P. ...

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  6. From the focus of parabola y^2 = 8x as centre, a circle is described s...

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  7. The straight line joining any point P on the parabolay^2=4ax to the ve...

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  8. The tangent and normal at P(t), for all real positive t, to the parabo...

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  9. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

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  10. Two parabolas y(2) = 4a(x – 1l(1)) and x(2) = 4a(y – l(2)) always touc...

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  11. Let A be the vertex and L the length of the latus rectum of the parabo...

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  12. The parametric coordinates of any point on the parabola y^(2) = 4ax ca...

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  13. The locus of the mid point of the focal radi of a variable point movin...

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  14. Two parabolas have the same focus. If their directrices are the x-axis...

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

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  16. Tangent to the parabola y^(2) = 4ax at point P meets the tangents at v...

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  17. A variable circle is described to passes through the point (1, 0) and ...

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