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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+1/t)^2` .

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NAGEEN PRAKASHAN ENGLISH-CONIC SECTION-Exercise 11B
  1. Find the equation of that parabol whose : (i) vertex is (0,0) and fo...

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  2. Find the vertex and axis of the parabola x^(2)-4x-3y+7=0.

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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 a point on the parabola y^(2)=8x, whose focal ...

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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 are on ...

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

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

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

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  19. Prove that the semi-latusrectum of the parabola y^2=4ax is the harmoni...

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