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The line joining A(bcosalpha,bsinalpha)a...

The line joining `A(bcosalpha,bsinalpha)andB(acosbeta,asinbeta)` is produced to the point M(x,y) such that `overline(AM):overline(BM)=b:a`, prove that `x+y"tan"(alpha+beta)/(2)=0`.

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CHHAYA PUBLICATION-REVISION OF PREVIOUS TWO DIMENSIONAL COORDINATE GEOMETRY -EXERCISE 1 ( Long Type Questions )
  1. Find the lenghts of the medians of the triangle whose vertices are (2,...

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  2. If (4,3) , (-2,7) and (0,11) are the coordinates of the mid -points o...

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  3. The line joining A(bcosalpha,bsinalpha)andB(acosbeta,asinbeta) is pro...

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  4. A(-1,5),B(3,1)and C(5,7) are the vertices of the DeltaABC. If D ,E and...

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  5. The coordinates of A , B , C are (6,3), (-3,5) and (4,-2) respectively...

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  6. The points P,Q,R are collinear , if the coordinates of P and Q be (3,4...

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  7. The coordinates of the points A,B,C D are respectively (6,3) , (-3,5) ...

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  8. The coordinates of the points A,B,C and D are (-2,3), (8,9), (0,4) and...

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  9. The coordinates of the points A and B are (3,4) and (5,-2) respective...

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  10. The area of a quadrilateral is 28 square unit. If the coordinates of i...

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  11. If x(1),x(2),x(3) as well as y(1),y(2),y(3) are in G.P. with the sa...

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  12. Shift the origin to a suitable point so that the equation 2x^(2)-4x+3y...

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  13. Find the point to which the origin should be shifted so that the equat...

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  14. Show that the distance between two points remains unaltered by the tra...

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  15. Reduce the equation x+y+5=0 andx-2y+2=0 to the form ax+by =0 by prope...

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  16. Choose a new origin (h,k) (retaining the directions of axes) so that t...

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  17. Find the distance between the point (1+sqrt2,1-sqrt2) and (0,0)

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  18. Show that the straight line joining the mid - points of two sides of a...

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  19. Show that the straight lines joining the mid - points of the opposite ...

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  20. Prove analytically that the area of a triangle is four times that of t...

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