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Consider a curve ax^2+2hxy+by^2=1 and a ...

Consider a curve `ax^2+2hxy+by^2=1` and a point P not on the curve. A line drawn from the point P intersects the curve at points Q and R. If the product PQ.PR is independent of the slope of the line, then show that the curve is a circle.

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Consider a curve ax^(2)+2hxy+by^(2)=1 and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If the product PQ.PR is independent of the slope of the line, then show that curve is a circle.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Consider a curve ax^2+2hxy+by^2=1 and a point P not on the curve. A li...

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  2. Determine whether the following represents a circle, a point or no cir...

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  3. Determine whether the following represents a circle, a point or no cir...

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  4. Determine whether the following represents a circle, a point or no cir...

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  5. Determine whether the following represents a circle, a point or no cir...

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  6. Determine whether the following represents a circle, a point or no cir...

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  7. Write the co-ordinates of the centre of the circle : 2x^2 + 2y^2-6x+8y...

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  8. Find the equations of the following circle : Centre (0, 2) and radiu...

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  9. In each of the following find the equation of the circle with centre (...

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  10. Find the equation of the circle with Centre (-2,3) and radius 4

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  11. Find the equations of the following circle : Centre (1,1) and radius...

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  12. Find the equations of the following circle : Centre (1/2,1/2) and ra...

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  13. Find the equations of the following circle : Centre (- a, -b) and ra...

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  14. The centre and radius of the circle x^2+(y-1)^2=2 are

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  15. Find the centre and radius of the circle : (x + 5)^2 + (y- 3)^2 = 36...

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  16. Find the centre and radius of the circle : (x-1/2)^2+ (y+ 1/3)^2 =1/...

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  17. Find the centre and radius of the circle : x^2 + y^2+ 8x + 10y- 8 =0...

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  18. Find the centre and radius of the circle : x^2 + y^2- 4x- 8y- 45 = 0...

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  19. Find the centre and radius of the circle : x^2 + y^2- 8x+ 10y- 12 = ...

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  20. Find the centre and radius of the circle : 2x^2 + 2y^2- x=0.

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  21. Show that the equation : Ax^2 + Ay^2 + Dx + Ey + F=0 represents a circ...

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