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Show that the point (x ,y) given by x=(2...

Show that the point `(x ,y)` given by `x=(2a t)/(1+t^2)a n dy=((1-t^2)/(1+t^2))` lies on a circle for all real values of `t` such that `-1lt=tlt=1,` where a is any given real number.

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VMC MODULES ENGLISH-CIRCLES-JEE ADVANCED ( ARCHIVE )
  1. Show that the point (x ,y) given by x=(2a t)/(1+t^2)a n dy=((1-t^2)/(1...

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  2. AB is a diameter of a circle and C is any point on the circumference o...

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  3. Find the equations of the circles passing through the point (-4,3) and...

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  4. Circles (s) touching the x-axis at a distance of 3 units from the orig...

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  5. Let C be any circle with centre (0,sqrt(2))dot Prove that at most two ...

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  6. about to only mathematics

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  7. A circle passes through three points A, B and C with the line segment ...

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  8. If (mi,1/mi),i=1,2,3,4 are concyclic points then the value of m1m2m3m4...

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  9. The abscisae of A and B are the roots of the equation x ^(2) + 2ax -b ...

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  10. about to only mathematics

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  11. If the two circles (x+1)^2+(y-3)^2=r^2 and x^2+y^2-8x+2y+8=0 intersect...

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  12. about to only mathematics

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  13. A circle S passes through the point 90,1) and is orthogonal to the cir...

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  14. Let ABCD be a square of side length 2 units. C2 is the circle through ...

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  15. A circle touches the line L and the circle C(1) externally such that b...

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  16. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  17. Match the conditions // expression in Column I with statement in Colum...

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  18. Let C1and C2 be two circles with C2 lying inside C1 A circle C lying i...

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  19. Three circles touch one another externally. The tangents at their poin...

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  20. A Tangent PT is drawn to the circle x^2 + y^2 =4 at point p(sqrt(3),1)...

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  21. A tangent PT is drawn to the circle x^(2)+y^(2)=4 at the point P( sqrt...

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