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By parallel transformation of coordinate axes to a properly chosen point (h,k), prove that the equation `12x^(2)-10xy+2y^(2)+11x-5y+2=0` can be reduced to one containing only terms of the second degree.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. The coordinates of A,B,C are (2,1) (6,-2) and (8,9) respectively. Find...

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  2. Find the equations to the straight lines passing through the foot of ...

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  3. By parallel transformation of coordinate axes to a properly chosen poi...

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  4. Show thathte coefficients of x^(2),xy and y^(2) "in" ax^(2)+2hxy+by^(2...

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  5. Prove that the area of the triangle with vertices (p,q),(x(1),y(1)) an...

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  6. The base of triangle passes through a fixed point (f,g) and its other ...

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  7. The straight line ax+by=1 intersect the circle x^(2)+y^(2)=c^(2) at P ...

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  8. The equations of two equal sides AB and AC of an isosceles triangle AB...

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  9. One diagonal of a square is the portion of the straight line 7x+5y=35 ...

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  10. If the straight lines a^(2)x+ay+k=0, b^(2) x+by+k=0 and c^(2)x+cy+k=0 ...

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  11. Show that the circle x^(2)+y^(2)-2y-15=0 lies completely within the ci...

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  12. Two sides of a rhombus ABCD are parallel to the lines x-y=5 and 6x-y=3...

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  13. Two sides of a rhombus lyin in the first quadrant are given by 3x-4y=0...

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  14. A line joining two points A (2,0) and B(3,1) is rotated about A in the...

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  15. A (3,0) and B(6,0) are two fixed points and P(x(1),y(1)) is a variable...

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  16. Find the coordinates of the centroid of the triangle, formed by the li...

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  17. The points (1,3) and (5,1) are two oppsite vertices of a rectangle. Th...

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  18. Show that the lines ax+by+c=0, ax-by+c=0, ax-by=c ax+ by-c=0 (a ne b) ...

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  19. Let A(ct(1), (c)/(t(1))), B(ct(2),(c)/(t(2))) and C(ct(3),(c)/(t(3))) ...

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  20. The circle A and B of a line segment of constant length c unit slides ...

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