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A point moves so that sum of the square...

A point moves so that sum of the squares of its distances from the vertices of a triangle is always constant. Prove that the locus of the moving point is a circle whose centre is the centroid of the given triangle.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. O(0,0) and A(4,4) are two given points and B is any point. Find the eq...

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  2. Show that the image of the point (h,k) with respect to the striaight l...

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  3. A point moves so that sum of the squares of its distances from the ve...

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  4. Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2...

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  5. A straight line is such that its segment between lines 5x-y-4=0 and 3x...

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  6. A rod of length a unit slides on the x-axis and another rod of length ...

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  7. A circle cuts intercepts of length 2a unit and 2b unit from the x-axis...

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  8. Let x^(2)+y^(2)-4x-2y-11=0 be a fixex circle.A pair of tangents to the...

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  9. The circle x^(2)+y^(2)-4x-4y+4=0 is inscribed in a triangle which has ...

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  10. Find the equation of the circle passing through the point (2,0) and to...

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  11. Tangents PQ and PR are drawn from the point (alpha, beta) to the circl...

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  12. Let S-=x^(2)+y^(2)+2gx+2fy+c=0 be a given circle. Find the of the foo...

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  13. The line 2x+3y=12 meets the x-axis at A and the y-axis at B. the line...

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  14. Find the equation of the line passing through the point (2,3) and maki...

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  15. Let ABC be a triangle with AB=AC. If D is the mid point of BC,E , foot...

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  16. Lines L(1)= ax+by+c=0 and L(2) -= lx+ mu+n=0 intersect at the point P ...

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  17. Detemine all values of alpha for which the point (alpha, alpha^(2)) li...

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  18. A line through A(-5-4) meets of lines x+3y+2=0, 2x+y+4 and x-y-5=0 at ...

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  19. Find the radius of the smallest circle which touches the straight lin...

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

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