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

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+1/t)^2`.

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NAGEEN PRAKASHAN-CONIC SECTION-Exercise 11B
  1. Find the vertex and axis of the parabola x^(2)-4x-3y+7=0.

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  2. Find the vertex, co-ordinates of focus, axis , directrix and latus rec...

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  3. Find the point on the parabola y^(2)=18x at which ordinate is 3 times ...

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  4. Find the point on the parabola y^(2)=12x at which ordinate is 3 times ...

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  5. The equations of the parabolas the extremities of whose latus rectum a...

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  6. Find the coordinates of points on the parabola y^2=8x whose focal dist...

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  7. Find the co-ordinates of the points lying on parabola y^(2)=16x whose ...

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  8. Find the co-ordinates of the points lying on parabola x^(2)=12y whose ...

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  9. If the parabola y^(2)=4ax passes through the point (2,-3) then find th...

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  10. Prove that the locus of mid-point of focal chords of parabola y^(2)=4a...

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  11. Show that y=ax^(2)+bx+c represents a parabola. Also find equation it...

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  12. Find the length of latus rectum of the parabola x^(2)=4x-4y.

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  13. Show that the equation (1)/(x+y-a)+(1)/(x-y+a)+(1)/(y-x+a)=0 repre...

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  14. Find the position of the following points with respect to the parabola...

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  15. Prove that the equation of the parabola whose vertex and focus lie on ...

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  16. Find the equation of the focal chord of the parabola y^(2)=8x whose mi...

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  17. Find the equation of the parabola whose vertex is (3,-6) and the equat...

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  18. Find the area of the triangle formed by the vertex and the ends of the...

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

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  20. Prove that the semi-latus rectum of a parabola is the harmonic mean of...

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