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:

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:

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:

The vertices of a triangles are A (x₁, x₁ tan α), B (x₂, x₂ tan β) and C (x₃,x₃ tan γ). If the circumcentre of Δ ABC coincides with the origin and H (a, b) be its orthocenter, then a/b is equal to: