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Tangents are drawn to the parabola at th...

Tangents are drawn to the parabola at three distinct points. Prove that these tangent lines always make a triangle and that the locus of the orthocentre of the triangle is the directrix of the parabola.

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CENGAGE ENGLISH-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=4a x at P such that it cuts the...

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

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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 dis...

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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 dot If L passes through the p...

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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+a)=...

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

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  15. If y+3=m1(x+2) and y+3=m2(x+2) are two tangents to the parabola y2=8...

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

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

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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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