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L O L ' and M O M ' are two chords of pa...

`L O L '` and `M O M '` are two chords of parabola `y^2=4a x` with vertex `A` passing through a point `O` on its axis. Prove that the radical axis of the circles described on `L L '` and `M M '` as diameters passes though the vertex of the parabola.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the range of values of lambda for which the point (lambda,-1) is ...

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  2. Prove that the locus of a point, which moves so that its distance from...

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  3. L O L ' and M O M ' are two chords of parabola y^2=4a x with vertex A ...

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

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

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  6. If three distinct normals can be drawn to the parabola y^2-2y=4x-9 fro...

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  7. Find the locus of thepoint of intersection of two normals to a parabol...

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  8. P(t1) and Q(t2) are the point t1a n dt2 on the parabola y^2=4a x . The...

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  9. Prove that the locus of the point of intersection of the normals at th...

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  10. Find the number of distinct normals that can be drawn from (-2,1) to t...

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  11. If the line passing through the focus S of the parabola y=a x^2+b x+c ...

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  12. If a focal chord of y^2=4a x makes an angle alpha in [0,pi/4] with the...

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  13. Find the length of the normal chord which subtends an angle of 90^@ at...

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  14. Find the locus of the point of intersection of the normals at the end ...

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  15. The abscissa and ordinates of the endpoints Aa n dB of a focal chord o...

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  16. If A B is a focal chord of x^2-2x+y-2=0 whose focus is S and A S=l1, t...

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  17. A circle is drawn to pass through the extremities of the latus rectum ...

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  18. Circles drawn on the diameter as focal distance of any point lying on...

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  19. If the length of a focal chord of the parabola y^2=4a x at a distance ...

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  20. Find the equation of the parabola whose focus is S(-1,1) and directrix...

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