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A variable circle is described to passes...

A variable circle is described to passes through the point (1, 0) and tangent to the curve `y = tan(tan^(-1)x)`. The locus of the centre of the circle is a parabola whose

A

length of the latus rectum is `2sqrt2`

B

axis of symmetry has the equation `x + y = 1`

C

vertex has the co-ordinates (3/4, 1/4)

D

none of these

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The correct Answer is:
B, C
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MOTION-PARABOLA-EXERCISE - II
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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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