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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

Axis

B

Directrix

C

Tangent at the vertex

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

AAKASH SERIES-REVISION EXERCISE -PARABOLA
  1. Show that length of perpendecular from focus 'S' of the parabola y^(2)...

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  2. If A,B,C are 3 points on a parabola , Delta 1 , Delta2 are the areas...

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

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  4. The tangent at 't' on the parabola y^(2) =4ax is parallel to a normal ...

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  5. The no. of normals drawn to (y-1) ^(2) =8 ( x+3) through (4,1 )

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  6. The normal at 'P' cuts the axis of the parabola y^(2) =4ax in G and S...

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  7. If two of the three feet of normals drawn from a point to the parabola...

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  8. The equation of a tangent to the parabola y^(2) =8x is y =x+2 . The po...

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  9. The locus of middle points of normal chords of the parabola y^(2) = 4...

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  10. If the normals at P and Q meet again on y^(2) =4ax at R then centro...

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  11. If the normal to y^(2) =4ax at t1 cuts the parabola again at t2 th...

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  12. Point of concurrence of the normals drawn at (2,8) , (128,64) , (162, ...

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  13. If ( x1, y1) , (x2, y2) ,(x3y3) are feet of the three normals drawn f...

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  14. If two normals drawn to the y^(2) =8x at ( 2,4) and (18, 12) intersec...

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  15. If the normals at P and Q meet again on the parabola y^(2) =4ax then ...

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  16. The shortest distance between the line y-x =1 and the curve x=y^2 is

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  17. If the parabola y^(2)=ax passes through (1, 2) then the equation of th...

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  18. A set of parallel chords of the parabola y^(2) =4ax have their mid-po...

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  19. If the angular bisectors of the coordinates axes cut the parabola y^(2...

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  20. If the straight line y=mx+c is parallel to the axis of the parabola y^...

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