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Prove that the orthocentre of the triang...

Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrix of the parabola

A

vertex

B

focus

C

foot of the directrix

D

none

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The correct Answer is:
B
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Show that the orthocentre of a triangle formed by three tangents to a parabola lies on the directrix.

Assertion (A) : Orthocentre of the triangle formed by any three tangents to the parabola lies on the directrix of the parabola Reason ® : The orthocentre of the triangle formed by the tangents at t_1, t_2 ,t_3 to the parabola y^(2) =4ax is (-a ( t_1+t_2+t_3+t_1t_2t_3) )

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The orthocentre of the triangle formed by (1,-3),(6,1),(4,-1) is

DIPTI PUBLICATION ( AP EAMET)-PARABOLA-EXERCISE 1 A
  1. The tangents to the parabola y^(2)=4ax at P(t(1)) and Q (t(2)) inters...

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  2. The orthocentre of the triangle formed by three tangents to the parabo...

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  3. Prove that the orthocentre of the triangle formed by any three tangent...

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  4. The feet of the perpendiculars drawn from the focus of a parabola to t...

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  5. If the distances of two points P and Q on the parabola y^(2) = 4ax fro...

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  6. If the distances of two points P and Q on the parabola y^(2) = 4ax fro...

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  7. If the distances of two points P and Q on the parabola y^(2) = 4ax fro...

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  8. PSQ is a focal chord of a parabola whose focus is S and vertex A . PA ...

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  9. If L,M,N are the three points on the parabola y^(2) = 4ax whose ordin...

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  10. The equation of the normal to the parabola y^(2)=8x at the point t is

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  11. The slope of the normal at (at^(2),2at) of the parabola y^(2)=4ax is

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  12. If the normal at t(1) on the parabola y^(2)=4ax meet it again at t(2)...

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  13. If the normal at t(1) on the parabola y^(2)=4ax meet it again at t(2)...

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  14. If the normal at (1,2) on the parabola y^(2)=4x meets the parabola aga...

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  15. If the normal to the parabola y^(2)=4x at P(1,2) meets the parabola a...

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  16. If the normals at the point t(1) and t(2) on y^(2)=4ax intersect at t...

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  17. The number of normals drawn to the parabola y^(2)=4x from the point (...

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  18. The number of normals that can be drawn through (-1,4) to the parabola...

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  19. From a point (C, 0) three normals are drawn to the parabola y^(2) = x....

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  20. If the tangents and normals at the extremities of a focal chord of a p...

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