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Prove that any three tangents to a parab...

Prove that any three tangents to a parabola whose slopes are in harmonic progression enclose a triangle of constant area.

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A DAS GUPTA-Parabola-EXERCISE
  1. Points A, B, C lie on the parabola y^2=4ax The tangents to the parabol...

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  2. If P, Q, R are three points on a parabola y^2=4ax whose ordinates are ...

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  3. Prove that any three tangents to a parabola whose slopes are in harmon...

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  4. Two straight lines are perpendicular to each other. One of them touche...

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  5. Find the equation of the chord to the parabola y^2=4axwhose middle poi...

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  6. Prove that the normal chord to a parabola at the point whose ordinate ...

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  7. Show that the area formed by the normals to y^2=4ax at the points t1,t...

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

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  9. For what values of 'a' will the tangents drawn to the parabola y^2 = 4...

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  10. Find the centre and radius of the smaller of the two circles that touc...

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  11. Prove that the length of the intercept on the normal at the point P(a ...

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  12. Prove that the locus of the middle pointsof chords of the parabolay^2=...

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  13. Prove that the locus of a point, which moves so that its distance from...

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  14. 5. The locus of point of intersection of two tangents to the parabola ...

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  15. Find the locus of the intersection of normals to the parabolay^2=4axat...

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  16. Find the locus of the point of intersection of those normals to the pa...

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  17. Find the locus of point of intersection of tangent to the parabola y^2...

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

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

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

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