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Prove that the locus of the centre of th...

Prove that the locus of the centre of the circle `(1)/(2)(x^(2)+y^(2))+xcostheta+ysintheta-4=0` is `x^(2)+y^(2)=1`

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ARIHANT MATHS-CIRCLE -Exercise For Session 1
  1. Evaluate the given limit lim(x to 0) (cosecx - cotx)

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  2. If the equation px^(2)+(2-q)xy+3y^(2)-6qx+30y+6q=0 represents a circle...

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  3. The equation of circle having centre at (2,2) and passes through the p...

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  4. One of the diameters of the circle x^2+y^2-12x+4y+6=0 is given by

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  5. If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle, then fi...

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  6. Area of the circle in which a chord of lengthsqrt2 makes an angle pi/2...

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  7. The lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 15...

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  8. If the lines 2x + 3y + 1 = 0 and 3x - y-4 = 0 lie along two diameters...

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  9. Find the derivative of function x^3 from first principle.

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  10. If a circle is concentric with the circle x^(2)+y^(2)-4x-6y+9=0 and pa...

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  11. Evaluate lim( x to pi) (tanx)/(x - pi/2)

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  12. Find lim(x to 0)f(x) , when f(x) = (5x + 2) .

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  13. Find the centre and radius of circle 5x^(2)+5y^(2)+4x-8y=16.

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  14. Prove that the centres of the circles x^2+y^2=1, x^2+y^2+6x-2y-1=0 and...

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  15. Find the equation of the circle having (1,-2) as its centre and passin...

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  16. Equation of circle passing through the centre of the circle x^2+y^2-4x...

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  17. Prove that the locus of the centre of the circle (1)/(2)(x^(2)+y^(2))+...

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  18. Find the equation of the following curves in cartesian form. If the cu...

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