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Prove that the locus of the middle point...

Prove that the locus of the middle point of portion of a normal to `y^(2) = 4ax` intercepted between the curve & the axis is another parabola. Find the vertex & the latus rectum of the second parabola.

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The correct Answer is:
(a,0);a
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MOTION-PARABOLA-EXERCISE - III
  1. From vertex O ofthe parabola y^2=4ax perpendicular is drawn at a tange...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. A fixed parabola y^(2) = 4ax touches a variable parabola. Find the equ...

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  17. Show that an infinite number of triangles can be inscribed in either o...

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  18. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

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  19. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

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  20. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

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