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Prove that it is impossible to have an e...

Prove that it is impossible to have an equilateral triangle for which of the coordinates of the vertices are all rational numbers.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. (3,2) and (-3,2) are the vertices of an equilateral triangle which con...

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  2. Show that the points A(a,b), B(a+alpha+ b,+ beta), C(a+alpha+ p, b+bet...

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  3. Prove that it is impossible to have an equilateral triangle for which ...

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  4. A straight line moves in such a way that the algebraic sum of the perp...

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  5. The coordinates of two point opposite vertices oc a square are (3,4) a...

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  6. If L,M,N divide the sides BC,CA and AB of a triangle ABC in the same r...

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  7. Find the equation to the locus represented by x=(2+t+1)/(3t-2), y=(t-1...

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  8. Find the equation to the locus represented by the parametric equation...

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  9. If t is a variable parameter, then the equation to the locus defined b...

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  10. The four point A(a,0), B(b,0) ,C(c,0) and D(d,0) are such that a and b...

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  11. The straight lines y=x=2 and y=6x+3 are parallel to two sides of the r...

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  12. The eqution of the side BC,CA and AB of the triangle ABC are u(1)=a(1)...

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  13. A striaght line intersect x-axis at A(7,0) and y-axis at B(0,-5). The ...

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  14. The equation of two diameters of a circle of area 154 sq unit are 2x-3...

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  15. If the four points (m(i),(1)/(m(i))) where m(1) gt 0 (I,1,2,3,4) are c...

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  16. The ends A and B of a rod AB of length 8 unit slide along the lines y=...

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  17. A is a point on the circle x^(2)+y^(2)=36. Find the locus of the point...

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  18. The coordinates of the points A and B are (1,3) and (-2,1) respectivel...

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  19. Find the equation of the diagonals of the parallelogram formed by the ...

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  20. Show that the lines y=0, sqrt(3y)-xy=sqrt(3) and sqrt(3y)+x-10=0 form ...

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