A And B Are Two Fixed Points. The Vertex C Of A Δ ABC moves Such That Cot A + Cot B = Constant. Locus Of C is A Straight Line:

Find the coordinates of the foot of the perpendicular from the point (2, 3) on the line y = 3x + 4.

Find the equation of the line passing through (a, b) and parallel to px +qy + 1 = 0.  

Find the equation of the line perpendicular to 3x + 4y + 1= 0 and passing through (1, 1).

Find the distance of line h (x + h) + k (y + k) = 0 from the origin.

Determine the distance between the lines : 6x + 8y – 45 = 0 and 3x + 4y – 5 = 0.

The algebraic sum of the perpendicular distances from A(x₁, y₁), B(x₂,y₂) and C(x₃, y₃) to a variable line is zero, then the line passes through:

If A (cos α, sin α), B (sin α, –cos α), C (1, 2) are the vertices of a ΔABC, then as α varies the locus of its centroid is:

The image of point (1, 3) in the line x + y – 6 = 0 is: 

If t₁, t₂, t₃ are distinct, then the points  are collinear if:

The number of integer values of m, for which the x-co-ordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is: