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Show that the locus of points such that ...

Show that the locus of points such that two of the three normals drawn from them to the parabola `y^2 = 4ax` coincide is `27ay^2 = 4(x-2a)^3`.

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A DAS GUPTA-Parabola-EXERCISE
  1. Find the locus of point of intersection of tangent to the parabola y^2...

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  2. Find the locus of the middle points of the chords of the parabola y^2=...

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  3. Show that the locus of points such that two of the three normals drawn...

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  4. Prove that the locus of the point of intersection of the normals at th...

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  5. Find the locus of the middle points of the chords of the parabola y^2=...

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  6. If two tangents to the parabola y^2=4ax from a point P make angles ...

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  7. Locus of the feet of the perpendiculars drawn from vertex of the parab...

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  8. If the focus =(2,3)and directrix is x+y=1 then the equation of the par...

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  9. The line x+y+1=0touches the parabola y^2=kx if k=.

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  10. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

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  11. Write the length of het chord of the parabola y^2=4a x which passes th...

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  12. Find the condition that the line x cosalpha + y sin alpha=p touches th...

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  13. The point of intersection of the tangents at the ends of the latus ...

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  14. Find the angle between the tangents drawn from (1, 3) to the parabola ...

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  15. Find the equation of the circle described on the line segment joining ...

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  16. A double ordinate of the parabola y^2 = 8px is of length 16p. The angl...

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  17. The equation of parabola whose vertex and focus lie on the axis of x a...

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  18. f the normal at the point P (at1, 2at1) meets the parabola y^2=4ax agu...

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  19. If the tangents to the parabola y^2=4axat the points (x1,y1)and ((x2,y...

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  20. Find the condition that the line x cosalpha + y sin alpha=p touches th...

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