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If the normals to the parabola y^2=4a x ...

If the normals to the parabola `y^2=4a x` at three points `P ,Q ,a n dR` meet at `A ,a n dS` is the focus, then `S PdotS qdotS R` is equal to `a^2S A` (b) `S A^3` (c) `a S A^2` (d) none of these

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The tangents to the parabola y^2=4a x at the vertex V and any point P meet at Q . If S is the focus, then prove that S PdotS Q , and S V are in GP.

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Tangents and normal drawn to the parabola y^2=4a x at point P(a t^2,2a t),t!=0, meet the x-axis at point Ta n dN , respectively. If S is the focus of theparabola, then (a) S P=S T!=S N (b) S P!=S T=S N (c) S P=S T=S N (d) S P!=S T!=S N

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. At what point on the parabola y^2=4x the normal makes equal angle with...

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  2. The focal chord to y^2=16 x is tangent to (x-6)^2+y^2=2. Then the poss...

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  3. If the normals to the parabola y^2=4a x at three points P ,Q ,a n dR m...

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  4. The locus of the midpoint of the segment joining the focus to a moving...

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  5. The curve described parametrically by x=t^2+t+1 , and y=t^2-t+1 repres...

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  6. Statement 1: The line y=x+2a touches the parabola y^2=4a(x+a) Stateme...

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  7. Consider a circle with its centre lying on the focus of the parabola, ...

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  8. Normal drawn to y^2=4a x at the points where it is intersected by the...

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  9. The radius of the circle touching the parabola y^2=x at (1, 1) and ha...

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  10. Maximum number of common normals of y^2=4ax and x^2=4by is

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  11. If two different tangents of y^2=4x are the normals to x^2=4b y , then...

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  12. The largest value of a for which the circle x^2+y^2=a^2 falls totally ...

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  13. A ray of light travels along a line y=4 and strikes the surface of cur...

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  14. A set of parallel chords of the parabola y^2=4a x have their midpoint ...

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  15. A line L passing through the focus of the parabola y^2=4(x-1) intersec...

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  16. The ration in which the line segement joining the points (4,-6) and (...

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  17. If (a , b) is the midpoint of a chord passing through the vertex of th...

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  18. A water jet from a function reaches it maximum height of 4 m at a d...

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  19. The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^...

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  20. A point P(x , y) moves in the xy-plane such that x=acos^2theta and y=2...

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