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Prove that diagonals of the parallelogra...

Prove that diagonals of the parallelogram formed by the four straight lines `sqrt(3)x+y=0, sqrt(3)y+x=0, sqrt(3)x+y=1 and sqrt(3)y+x=1` are the right angles to one another.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. The coordinates of the vertex A of the triangle ABC are (-5,2) the equ...

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  2. The coordinates of the vertices of a triangle are [at(1)t(2),a(t(1)+t(...

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  3. Prove that diagonals of the parallelogram formed by the four straight ...

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  4. Find the locus of the foot of the perpendicular from the origin upon ...

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  5. Show that for all values of a,b and c the line (b-c)x+(c-a)y+a-b=0 alw...

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  6. Show that the locus of the point of intersection of the stright lines ...

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  7. Prove analytically that in any triangle the perpendiculars drawn from ...

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  8. Prove analytically that the bisectors of the interior angles of a tria...

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  9. If d(1),d(2),d(3) be the distances of a fixed point from the straight ...

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  10. Show that the quadrilateral formed by the four lines y=mx+a sqrt(a+m^(...

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  11. Show that the lines x cos alpha+ y alpha=p, x cos (alpha+ (2pi)/(3)) +...

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  12. 2x-y+4=0 is a diameter of a circle which circumscribes a rectangle ABC...

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  13. ABC is right-angle triangle, right -angled at A. The coordinates of B ...

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  14. The line through A( a cos theta,0) and perpendicular to the x-axis mee...

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  15. P and Q are two point on the line x-y+1=0, if O is the origin and bar...

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  16. O(0,0) and A(4,4) are two given points and B is any point. Find the eq...

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

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

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

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

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