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Find the locus of point of intersection of tangent to the parabola `y^2=4ax` (i)which are inclined at an angle `theta` to each other. (ii) which intercept constant length c on the tangent at the vertex (iii) such that the area of `DeltaABC` is constant c; where A and B are the points of intersection of tangents with the y-axis and R is a point of intersections of tangents.

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Find the locus of point of intersection of tangent to the parabola y^2=4ax which are inclined at an angle theta to each other.

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A DAS GUPTA-Parabola-EXERCISE
  1. Find the locus of the intersection of normals to the parabolay^2=4axat...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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