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‘O’ is the vertex of the parabola y^(2) ...

‘O’ is the vertex of the parabola `y^(2) = 4ax` & L is the upper end of the latus rectum. If LH is drawn perpendicular to OL meeting OX in H, prove that the length of the double ordinate through H is `4asqrt5` .

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MOTION-PARABOLA-EXERCISE - III
  1. ‘O’ is the vertex of the parabola y^(2) = 4ax & L is the upper end of ...

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  2. Through the vertex 'O' of parabola y^2=4x, chords OP and OQ are drawn...

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  3. Find the equations of the chords of the parabola y^2= 4ax which pass t...

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  4. Find the equations of the tangents to theparabola y= 16x, which are pa...

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  5. Find the equation of tangents of the parabola y^2=12 x , which passes ...

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  6. From vertex O ofthe parabola y^2=4ax perpendicular is drawn at a tange...

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  7. Let P be a point on the parabola y^(2) - 2y - 4x+5=0, such that the ta...

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  8. Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex...

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  9. Show that the normals at the points (4a, 4a) & at the upper end of t...

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  10. In the parabola y^(2) = 4ax, the tangent at the point P, whose absciss...

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  11. Prove that the locus of the middle point of portion of a normal to y^(...

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  12. Three normals to y^2=4x pass through the point (15, 12). Show that one...

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  13. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

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  14. Prove that, the normal to y^(2) = 12x at (3,6) meets the parabola agai...

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  15. P & Q are the points of contact of the tangents drawn from the point T...

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  16. A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to th...

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  17. Show that the normals at two suitable distinct real points on the para...

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  18. Let S is the focus of the parabola y^(2) = 4ax and X the foot of the d...

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  19. Prove that the parabola y^(2) = 16x and the circle x^(2) + y^(2) - 40x...

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  20. .Find the equation ofthe circle which passes through the focus ofthe p...

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