Consider The Family Of Lines             (x + y – 1) + λ (2x + 3y – 5) = 0 And   (3x + 2y – 4) + µ (x + 2y – 6) = 0   Equation Of A Straight Line That Belongs To Both The Families Is:

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 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:

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:

A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinates axes at points P and Q. As L varies, the absolute minimum values of OP + OQ is (O is origin)

If p₁, p₂, p₃ be the length perpendicular from the points

(m², 2m), (mm’, m + m’) and (m’², 2m’)

respectively on the line