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Prove that the locus of the point of int...

Prove that the locus of the point of intersection of the normals at the ends of a system of parallel chords of a parabola is a straight line which is a normal to the curve.

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A DAS GUPTA-Parabola-EXERCISE
  1. Find the locus of the middle points of the chords of the parabola y^2=...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. The angle between the tangents drawn from the origin to the parabola y...

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