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Show that the lines ax+by+c=0, ax-by+c=0...

Show that the lines `ax+by+c=0, ax-by+c=0, ax-by=c ax+ by-c=0 (a ne b)` enclose a rhombus whose area is `(2c^(2))/(ab)` sq unit.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Find the coordinates of the centroid of the triangle, formed by the li...

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

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

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

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  6. A variable striaght line of slope 4 intresects the hyprbola xy=1 at tw...

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  7. If x cos alpha+ y sin alpha=p, where p=(-sin^(2) alpha)/(cos alpha) be...

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  8. A tangent drawn from the point (4,0) to the circle x^(2)+y^(2)=8 touch...

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  9. A(x(1) y(1)) and B(x(2), y(2)) are two given points on a circle. If th...

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  10. If 4a^(2)-5b^(2)+6a+1=0 find the equation of the circle for which the...

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  11. Find the point of the circle x^(2)+y^(2)-6x+4y=0 which is (i) nearest ...

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  12. Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2...

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  13. Vertices A(1,1) , B(4,-2) and (5,5) of a triangle are given , find the...

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  14. Prove that the locus of middle points of chords of constant length 2d ...

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  15. Find the integer values of m for which x-coordinate of the point of in...

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  16. A chord AB of the circle x^(2)+y^(2)=a^(2) subtends a right angle at i...

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  17. The corodinates of the three vertices of a triangle are (a, a tan alph...

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  18. The triangle PQR is inscribed in the circle x^(2)+y^(2)=25. If Q and ...

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  19. Let L(1) be a striaght line passing through the origin and L(2) be the...

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  20. A rectangle PQRS has its side PQ paralle to the line y=mx and vertices...

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