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The equation of two side of a triangle a...

The equation of two side of a triangle are `y=m_(1) x and y= m_(2)x`, where `m_(1) and m_(2)` are two roots of the equation `bx^(2)+2hx+a=0`. If the orthocentre of the triangle be (a,b) , then show that the equation of the third side of the triangle is `(a+b)(ax+by) =ab(a+b-2h)`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. If a circle passes through the points of intersection of the coordinat...

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  2. Let a circle be given by 2x(x-a)+y(2y-b)=0 ( a ne 0, b ne 0). Find the...

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  3. The equation of two side of a triangle are y=m(1) x and y= m(2)x, wher...

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  4. In a triangle ABC, coordinates of A are (1,2) and the equations of the...

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  5. One diagonal of a square is the portion of the line (x)/(a)+(y)/(b)=1....

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  6. A circle of radius r passes through the origin and intersects the x-ax...

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  7. The coordinates of A,B,C are (2,1) (6,-2) and (8,9) respectively. Find...

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

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

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

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

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

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

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

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

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

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

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

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

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