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Suppose a point (x(1),y(1)) satisfies x^...

Suppose a point `(x_(1),y_(1))` satisfies `x^(2)+y^(2)+2gx+2fy+c=0` then show that it represents a circle whenever g,f and c are real.

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represents a circle.
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AAKASH SERIES-CIRCLES-PRACTICE EXERCISE
  1. Suppose a point (x(1),y(1)) satisfies x^(2)+y^(2)+2gx+2fy+c=0 then sho...

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  2. The circle with centre (1,1) and radius 1 is

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  3. For a circle two diameter are x+y=3, x-y=1 then centre is

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  4. Circle with centre (-1,2) and passing through origin is

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  5. The equation of the circle concentric with x^(2)+y^(2)-6x+4y-3=0 and h...

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  6. The equation of the circle concentric with x^(2)+y^(2)-2x+8y-23=0 and ...

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  7. For the circle x^(2)+y^(2)-4x+2y+c=0 radius is 4 then c=

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  8. If A(1),A(2),A(3) be the areas of circles x^(2)+y^(2)+4x+6y-19=0, x^(2...

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  9. The equation of the circle with centre (2,3) and distance between (0,0...

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  10. The equation of the circle with radius 4 and centres as the midpoint o...

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  11. The circle with centre (1,-3) and radius being the distance between th...

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  12. If the area of the circle x^(2)+y^(2)+4x+2y+k=0 is 5pi square cms then...

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  13. If (2,3) is an extremity of a diameter of the circle x^(2)+y^(2)-5x-8y...

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  14. The line x/a+y/b=1 meets the axis of and y at A and B respectively and...

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  15. Equation of circle with centre (-1,2) and passing through the centroid...

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  16. The centroid of an equilateral triangle is (0, 0) and the length of th...

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  17. Equation of the circle with radius 10 and whose two diameters are x+y=...

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  18. If a circle is inscribed in a square of side 10, so that the circle t...

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  19. Show that the equation of the circle which pass through the points (1,...

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  20. If the abscissae of points A, B are the roots of the equation x^(2) + ...

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  21. The abscissae of two points A and B are the roots of the equation x^(2...

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