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Let a circle be given by 2x(x-a)+y(2y-b)...

Let a circle be given by `2x(x-a)+y(2y-b)=0 ( a ne 0, b ne 0)`. Find the condition on a and b if two chords, each bisected by the x-axis, can be drawn to the circle from `(a,(b)/(2))`.

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The correct Answer is:
`a^(2)-2b^(2) gt0`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Find the radius of the smallest circle which touches the straight lin...

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  2. If a circle passes through the points of intersection of the coordinat...

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  3. Let a circle be given by 2x(x-a)+y(2y-b)=0 ( a ne 0, b ne 0). Find the...

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  4. The equation of two side of a triangle are y=m(1) x and y= m(2)x, wher...

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  5. In a triangle ABC, coordinates of A are (1,2) and the equations of the...

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  6. One diagonal of a square is the portion of the line (x)/(a)+(y)/(b)=1....

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  7. A circle of radius r passes through the origin and intersects the x-ax...

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  8. The coordinates of A,B,C are (2,1) (6,-2) and (8,9) respectively. Find...

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  9. Find the equations to the straight lines passing through the foot of ...

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  10. By parallel transformation of coordinate axes to a properly chosen poi...

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  11. Show thathte coefficients of x^(2),xy and y^(2) "in" ax^(2)+2hxy+by^(2...

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  12. Prove that the area of the triangle with vertices (p,q),(x(1),y(1)) an...

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  13. The base of triangle passes through a fixed point (f,g) and its other ...

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  14. The straight line ax+by=1 intersect the circle x^(2)+y^(2)=c^(2) at P ...

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  15. The equations of two equal sides AB and AC of an isosceles triangle AB...

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  16. One diagonal of a square is the portion of the straight line 7x+5y=35 ...

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  17. If the straight lines a^(2)x+ay+k=0, b^(2) x+by+k=0 and c^(2)x+cy+k=0 ...

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  18. Show that the circle x^(2)+y^(2)-2y-15=0 lies completely within the ci...

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  19. Two sides of a rhombus ABCD are parallel to the lines x-y=5 and 6x-y=3...

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  20. Two sides of a rhombus lyin in the first quadrant are given by 3x-4y=0...

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