If a, b, c are Unequal And Different From 1 Such That The Points  are Collinear, Then  

The number of integral points (integral point means both the coordinates should be integer) that lie exactly in the interior of the triangle with vertices (0, 0), (0, 21), and (21, 0) is

Let P = (–1, 0), Q = (0, 0) and R =  be three points. Then the equation of the bisector of the angle PQR is 

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio.

Let A₀, A₁ A­₂ A₃ A₄ A₅ be a regular hexagon described in a circle of unit radius. Then the product of the length of the line segments A_0­ A₁, A₀ A₂and A₀ A₄ is 

The diagonals of a parallelogram PQRS are long the lines

x + 3y = 4 and 6x – 2y = 7, then PQRS must be a

The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is 

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a² + 1, a² + 1) and (2a, –2a), then the orthocenter lies on the line.

If two vertices of a triangle are (–2, 3) and (5, –1), orthocentre lies at the origin and centroid on the line x + y = 7, then the third vertex lies at