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Find the equation to the straight line parallel to 3x − 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, −1).
Concept: undefined >> undefined
Prove that the lines 2x − 3y + 1 = 0, x + y = 3, 2x − 3y = 2 and x + y = 4 form a parallelogram.
Concept: undefined >> undefined
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Find the angle between the lines x = a and by + c = 0..
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Find the equation of the line mid-way between the parallel lines 9x + 6y − 7 = 0 and 3x + 2y + 6 = 0.
Concept: undefined >> undefined
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 \[\left| \frac{\left( d_1 - c_1 \right)\left( d_2 - c_2 \right)}{a_1 b_2 - a_2 b_1} \right|\] sq. units.
Deduce the condition for these lines to form a rhombus.
Concept: undefined >> undefined
Prove that the area of the parallelogram formed by the lines 3x − 4y + a = 0, 3x − 4y + 3a = 0, 4x − 3y− a = 0 and 4x − 3y − 2a = 0 is \[\frac{2}{7} a^2\] sq. units..
Concept: undefined >> undefined
Show that the diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n' = 0, mx + ly + n = 0 and mx + ly + n' = 0 include an angle π/2.
Concept: undefined >> undefined
Show that the point (3, −5) lies between the parallel lines 2x + 3y − 7 = 0 and 2x + 3y + 12 = 0 and find the equation of lines through (3, −5) cutting the above lines at an angle of 45°.
Concept: undefined >> undefined
Write an equation representing a pair of lines through the point (a, b) and parallel to the coordinate axes.
Concept: undefined >> undefined
Three vertices of a parallelogram taken in order are (−1, −6), (2, −5) and (7, 2). The fourth vertex is
Concept: undefined >> undefined
The following example is the null set example or not?
Set of even prime numbers
Concept: undefined >> undefined
The following example is the null set example or not?
{x : x is a natural numbers, x < 5 and x > 7}
Concept: undefined >> undefined
The following example is the null set example or not?
{y : y is a point common to any two parallel lines}
Concept: undefined >> undefined
Identify whether the following set is finite or infinite.
The set of months of a year
Concept: undefined >> undefined
Identify whether the following set is finite or infinite.
{1, 2, 3, ...}
Concept: undefined >> undefined
Identify whether the following set is finite or infinite.
{1, 2, 3, ... 99, 100}
Concept: undefined >> undefined
Identify whether the following set is finite or infinite.
The set of positive integers greater than 100.
Concept: undefined >> undefined
