On The Portion Of The Straight Line x + y = 2 Which Is Intercepted Between The Axes, A Square Is Constructed, Away From The Origin, With This Portion As One Of Its Side. If p denotes The Perpendicular Distance Of A Side Of This Square From The Origin, Then The Maximum Value Of p is 

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 

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   

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

Let O be the origin, A (1, 0) and B (0, 1) and P (x, y) are points such thatxy > 0 and x + y < 1, then

If a line joining two points A (2, 0) and B (3, 1) is rotated about A in anticlockwise direction through and angle 15^o, then equation of the line is the new position is

An equation of a line through the point (1, 2) whose distance from the point (3, 1) has the greatest value is

Let 0 < α < π/2 be a fixed angle. If P = (cos θ, sin θ) and Q = (cos (α – θ), sin (α – θ) then Q is obtained from P by

The line x + y = 1 meets x-axis at A and y-axis at B, P is the mid-point ofAB (Fig). P_1­ is the foot of the perpendicular from P to OA; M₁ is that from P₁ to OP; P₂ is that from M₁ to OA; M₂ is that from P₂ to OP; P₃is that from M₂ to OA and so on. If P_n denotes the nth foot of the perpendicular on OA from M_{n – 1}, then OP_n =