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If the point (at^2,2at) be the extremity...

If the point (`at^2,2at`) be the extremity of a focal chord of parabola `y^2=4ax` then show that the length of the focal chord is `a(t+t/1)^2` .

A

`a{t_1+1/t_1}^2`

B

`a{t_1-1/t_1}^2`

C

`2at_1`

D

`2a//t_1`

Text Solution

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The correct Answer is:
A
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ML KHANNA-THE PARABOLA -Problem Set (3) (MULTIPLE CHOICE QUESTIONS)
  1. The equation of a normal to the parabola y=x^(2)-6x+6 which is perpend...

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  2. If the normals at two points P and Q of a parabola y^2 = 4ax intersect...

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  3. If the point (at^2,2at) be the extremity of a focal chord of parabola ...

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  4. A triangle ABC of area Delta is inscribed in the parabola y^2 = 4ax s...

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  5. The locus of the middle points of the focal chord of the parabola y^(2...

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  6. The locus of the poles of focal chords of the parabola y^2 = 4ax is

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  7. A focal chord of parabola y^(2)=4x .is inclined at an angle of (pi)/(4...

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  8. The length of the subnormal to the parabola y^(2)=4ax at any point is ...

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  9. Find the locus of the mid-points of the chords of the parabola y^2=4ax...

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  10. The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k...

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  11. If the normals any point to the parabola x^(2)=4y cuts the line y = 2 ...

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  12. The locus of the mid-points of the portion of the normal to the parabo...

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  13. Through the vertex O of a parabola y^2 = 4x chords OP and OQ are draw...

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  14. Tangents are drawn from any point on the line x + 4a=0 to the parabola...

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  15. A is a point on the parabola y^2 = 4ax The normal at A cuts the parabo...

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  16. The length of the normal chord to the parabola y^2 = 4x which subtends...

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  17. A variable chord PQ of the parabola y^2 = 4ax subtends a right angle ...

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  18. The locus of point of intersection of two normals drawn to the parabol...

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  19. P ,Q , and R are the feet of the normals drawn to a parabola (y-3)^2=8...

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  20. If two different tangents of y^2 = 4x are the normals to the parabola...

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