The Line x + y = 1 Meets x-axis At A and y-axis At B, P is The Mid-point OfAB (Fig). P1­ 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 Pn denotes The nth Foot Of The Perpendicular On OA from Mn – 1, Then OPn =  

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

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 

The line x + y = a, meets the axis of x and y at A and B respectively. A triangle AMN is inscribed in the triangle OAB, O being the origin, with right angle at N. M and N lie respectively on OB and AB. If the area of the triangle AMN is 3/8 of the area of the triangle OAB, then AN/BN is equal to.