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Tangents are drawn to the parabola at th...

Tangents are drawn to the parabola at three distinct points.
Prove that the orthocentre of the triangle formed by points of intersection of tangents always lies on the directrix.

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the radius of the largest circle, which passes through the focus ...

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  2. A tangent is drawn to the parabola y^(2)=4ax at P such that it cuts th...

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  3. Tangents are drawn to the parabola at three distinct points. Prove t...

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  4. Statement 1: The circumcircle of a triangle formed by the lines x=0,...

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  5. Statement 1: The point of intersection of the tangents at three dist...

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  6. Statement 1: If the straight line x=8 meets the parabola y^2=8x at Pa ...

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  7. Statement 1: Normal chord drawn at the point (8, 8) of the parabola ...

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  8. Statement 1: The value of alpha for which the point (alpha,alpha^2) li...

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  9. Statement 1: If there exist points on the circle x^2+y^2=a^2 from whic...

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  10. Let L be a normal to the parabola y^(2)=4x. If L passes through the po...

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  11. Let P and Q be distinct points on the parabola y^2 = 2x such that a c...

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  12. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

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  13. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+c)=0 ...

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  14. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

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  15. If y+3=m1(x+2) and y+3=m2(x+2) are two tangents to the parabola y^2=8x...

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  16. A line of slope lambda(0 < lambda < 1) touches the parabola y+3x^2=0 a...

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  17. If y=2x-3 is tangent to the parabola y^(2)=4a(x-(1)/(3)), then a is eq...

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  18. The straight lines joining any point P on the parabola y^2=4a x to the...

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  19. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

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  20. A tangent is drawn to the parabola y^2=4 x at the point P whose abscis...

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