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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

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the orthocenter of the triangle `PQR`, with abscissa as `-a`, lies on the directrix of the parabola.
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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) )

The orthocentre of the triangle formed by (0,0),(5,-1),(-2,3) is

AAKASH SERIES-PARABOLA-SOLVED EXAMPLES
  1. The normals from (P,0) are drawn to the parabola y^(2) = 8x, one of th...

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  2. Show that the locus of point of intersection of perpendicular tangents...

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  3. Show that the equation of the common tangent to the circle x^(2) + y^(...

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  4. The locus of the foot of the perpendicular from the focus to the tange...

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  5. Show that straight line 7x+6y=13 is a tangent to the parabola y^(2)-7x...

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  6. Find the condition for the line y=mx+c to be a tangent to the parabola...

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  7. If a chord of the parabola y^(2) = 4ax touches the parabola y^(2) = 4b...

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  8. Prove that two parabolas y(2)=4ax "and" x^(2)=4by intersect (other tha...

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  9. Show that the focal chord of the parabola y^(2)=4ax, which makes an an...

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  10. Show that semi latus rectum of the parabola y^(2) =4ax is the harmonic...

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  11. Prove that the locus of point of intersection of two perpendicular nor...

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  12. If ((1)/(2),2) is one extermity of a focalchord of the parabola y^(2)=...

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  13. Prove that the point on the parabola y^(2) = 4a ( a gt 0 nearest to th...

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  14. Two parabolas have the same vertex and equal lengh of latus rectum su...

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  15. The sum of the ordinates of two points on y(2)=4ax is equal to the sum...

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  16. Prove that the portion of the tangent intercepted between the point of...

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  17. Prove that the radius of the circle whose centre is (-4,0) and which c...

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  18. A triangle ABC of area Delta is inserted in the parabola y^(2) =4ax su...

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  19. Prove that the circle on a focal radius of a parabola, as diameter tou...

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

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