If P is A Point (x, y) On The Line, y = –3x such That P and The Point (3, 4) Are On The Opposite Sides Of The Line 3x – 4y = 8, Then     

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 a, b, c are unequal and different from 1 such that the points  are collinear, then  

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

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p andq are the intercepts of the line L on the new axes, then 

The area enclosed by 2|x| + 3|y| ≤ 6 is