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If (x(1),y(1)),(x(2),y(2)),(x(3),y(3))an...

If `(x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3))and(x_(4),y_(4))` be the consecutive vertices of a parallelogram , show that , `x_(1)+x_(3)=x_(2)+x_(4)andy_(1)+y_(3)=y_(2)+y_(4)`.

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If (x_(1),y_(1),z_(1)) , (x_(2),y_(2),z_(2)) , (x_(3) ,y_(3),z_(3)) and (x_(4) , y_(4) , z_(4)) be the consecutive vertices of a parallelogram, show that x_(1)+x_(3)=x_(2)+x_(4),y_(1)+y_(3)=y_(2)+y_(4) and z_(1)+z_(3)=z_(2)+z_(4) .

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Normals at (x_(1),y_(1)),(x_(2),y_(2))and(x_(3),y_(3)) to the parabola y^(2)=4x are concurrent at point P. If y_(1)y_(2)+y_(2)y_(3)+y_(3)y_(1)=x_(1)x_(2)x_(3) , then locus of point P is part of parabola, length of whose latus rectum is __________.

Three points P (h, k), Q(x_(1) , y_(1))" and " R (x_(2) , Y_(2)) lie on a line. Show that (h - x_(1)) (y_(2) - y_(1)) = (k - y_(1)) (x_(2) - x_(1)) .

If x_(1),x_(2),x_(3) as well as y_(1),y_(2),y_(3) are in A.P. with the same common difference , then show that the points (x_(1),y_(1)),(x_(2),y_(2))and(x_(3),y_(3)) are collinear.

If x_(1),x_(2),x_(3) as well as y_(1),y_(2),y_(3) are in G.P. with the same common ratio , then show that the points (x_(1),y_(1)),(x_(2),y_(2))and(x_(3),y_(3)) lie on a straight line .

If y= 3 cos (log x)+4 sin(log x) , show that x^(2)y_(2)+xy_(1)+y=0 .

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CHHAYA PUBLICATION-REVISION OF PREVIOUS TWO DIMENSIONAL COORDINATE GEOMETRY -EXERCISE 1 (Very Short Type Questions )
  1. The line -segment overline(CD) is produced to Q such that 2overline(CQ...

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  2. Find the coordinates of the point of trisection of the line - segment ...

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  3. Show that the line -segment joining the points (8,3),(-2,7) and the li...

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  4. Find (x,y) if (3,2) , (6,3) , (x,y) and (6,5) are the vertices of a pa...

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  5. If (x(1),y(1)),(x(2),y(2)),(x(3),y(3))and(x(4),y(4)) be the consecutiv...

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  6. Find the coordinates of the point of intersection of the medians of th...

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  7. The coordinates of the vertices of a triangle are (4,-3) , (-5,2) and...

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  8. The centroid of a triangle is (-1,-2) and coordinates of its two verti...

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  9. The coordinates of the vertices A ,B and C of the triangle ABC are (-...

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  10. For what value of k the points (1,-1) , (2,1) and (k,5) shall be on th...

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  11. If the points (a,0),(0,b) and (1,1) are collinear , then show that (1...

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  12. If the points (1,2) and (2,4) and (t,6) be collinear , find the value ...

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  13. Find the area of the triangle having vertices (1,4) , (-1,2)and (-4,-1...

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  14. Find the area of the triangle having vertices (a,b+c), (b,c+a) and (c,...

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  15. Show that the straight line joining the points (-3,2) and (6,-4) pass...

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  16. Examine the collinearity of the point (2,3),(4,5),and (6,5) .

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  17. If the A and B have coordinates (a costheta,bsintheta)and (-asintheta...

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  18. What does the eqution (x)/(a)+(y)/(b)=2 become if the axes are transf...

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  19. A point moves in the xy - plane in such a way that its distances from ...

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  20. A point moves such that its distance from the y-axes is equal to its d...

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