The straight line passing through the point of intersection of the straight lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and having infinite slope and at a distance 2 unit from the origin has the equation
x = 2
Any line through the intersection of the given line is
P + λQ = 0
or (x – 3y +1) + λ(2x + 5y – 9) = 0
Its slope will be infinite if it is perpendicular to x-axis i.e. parallel to y-axis.
Hence the coefficient of y will be zero.
Putting for λ the line is x = 2 clearly its distance from (0, 0) is 2.
The equation to the side of a triangle are x – 3y = 0, 4x + 3y = 5 and 3x + y = 0. The line 3x – 4y = 0 passes through
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A point equidistant from the lines 4x + 3y + 10 = 0, 5x – 12y + 26 = 0 and 7x + 24y – 50 = 0 is
Let P = (–1, 0), Q = (0, 0) and be three points. Then the equation of the bisector of the angle PQR is
Area of Δ formed by line x + y = 3 and bisectors of pair of straight lines x2 – y2 +2y = 1is
The equation of the straight line which passes through the point (1, –2) and cuts off equal intercepts from the axes will be
The three lines 3x + 4y + 6 = 0, and 4x + 7y + 8 = 0 are
The line (p + 2q)x + (p – 3q)y = p – q for different values of p and qpasses through the point
The locus of the mid-point of te portion intercepted between the axes by the line where p is constant is
shifting of origin (0, 0) to (h, k)
Rotation of axes through an angle θ.
1:- by rotating the axes through an angle θ the equation xy – y2 – 3y + 4 = 0 is transformed to the from which does not contain the term of xy then ….