Equation passes through (0, 0) and make an angle of 45Ā° with the line ā3x + y = 11. Since, the equations of two lines passing through a point x1,y1 and making an angle Ī± with the given line y = mx +...
Exercise 23.17
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Prove that the area of the parallelogram formed by the lines a1x + b1y + c1 = 0, a1x + b1y + d1 = 0, a2x + b2y + c2 = 0, a2x + b2y + d2 = 0 is (FIG 1)sq. units. Deduce the condition for these lines to form a rhombus.
FIG 1: SOLUTION: The given lines are \[\begin{array}{*{35}{l}} {{a}_{1}}x\text{ }+\text{ }{{b}_{1}}y\text{ }+\text{ }{{c}_{1}}~=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)Ā \\ {{a}_{1}}x\text{...
Prove that the area of the parallelogram formed by the lines 3x ā 4y + a = 0, 3x ā4y + 3a = 0, 4x ā 3y ā a = 0 and 4x ā 3y ā 2a = 0 is 2a2/7 sq. units.
The given lines are \[\begin{array}{*{35}{l}} 3x~-~4y\text{ }+\text{ }a\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)Ā \\ 3x~-~4y\text{ }+\text{ }3a\text{ }=\text{ }0\text{ }\ldots \text{...
Show that the diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + nā = 0, mx + ly + n = 0 and mx + ly + nā = 0 include an angle Ļ/2.
The given lines are \[\begin{array}{*{35}{l}} lx\text{ }+\text{ }my\text{ }+\text{ }n\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)Ā \\ mx\text{ }+\text{ }ly\text{ }+\text{ }n\text{...