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The locus of middle points of a family of focal chord of the parabola `y^(2) =4 ax` is-

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The locus of the middle points of the focal chords of the parabola, y^2=4x is:

Show that the product of the ordinates of the ends of a focal chord of the parabola y^(2) = 4ax is constant .

The locus of the midpoints of all chords of the parabola y^(2) = 4ax through its vertex is another parabola with directrix is

Show that the locus of the middle points of chords of the parabola y^(2) = 4ax passing through the vertex is the parabola y^(2) = 2ax

Show that the locus of the middle points of chords of the parabola y^(2) = 4ax passing through the vertex is the parabola y^(2)= 2ax .

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

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

Length of the shortest normal chord of the parabola y^2=4ax is

If (at^(2) , 2at) be the coordinate of an extremity of a focal chord of the parabola y^(2) =4ax, then the length of the chord is-

Prove that the the middle points of the normal chords of the parabola y^(2)=4ax is on the curve (y^(2))/(2a)+(4a^(3))/(y^(2))=x-2a

PATHFINDER-PARABOLA, ELLIPSE AND HYPERBOLA-QUESTION BANK
  1. Find the coordinates of vartex and the length of latus rectum of the p...

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  2. If theta is a variable paramete, then the equations x= 1/4(3- cosec ^(...

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  3. The locus of middle points of a family of focal chord of the parabola ...

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  4. The coordinates of the two ends of latus rectum of a parabola are (8,1...

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  5. A parabola passes through the points (0.0) ,(2,2) and (-2,-6) and it...

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  6. If (at^(2) , 2at) be the coordinate of an extremity of a focal chord o...

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  7. The directrix of a parabola is x + y + 4 = 0 and vertix is the point (...

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  8. Show that the equation of the chord of the parabola y^2=4ax through th...

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  9. The pt. (2+4costheta, 1+2sintheta) represents the parametric coordinat...

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  10. If eccentricities of the ellipse x^2/36+y^2/25=1 and x^2/a^2+y^2/b^2=1...

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  11. The length of the latus rectum of the ellipse 2x^2+4y^2=16 is

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  12. The coordinates of the foci of the ellipse 20x^2+4y^2=5 are

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  13. The length of the semi-major axis of an ellipse is 13 and its eccentri...

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  14. The eccentricy of the ellipse x^2+4y^2+2x-24y+33=0 is

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  15. find the length of the latus rectum of the ellipse (x^(2))/(9) +(y^(...

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  16. The coordinates of the point on the ellipse 9x^(2) + 16y^(2) = 144 ...

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  17. If the distance between the foci of an ellipse is equal to the length ...

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  18. Find the eccentricity, the length of latus rectum and the centre of e...

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  19. Find the eccentricity of the ellipse if the length of minor axis ...

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  20. The eccentricity of an ellipse whose distance between the foci is 4 an...

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