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.

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 = 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 =  

The point (4, 1) undergoes the following transformation successively.

(i) Reflection about the line y = x

(ii) Translation through a distance 2 units along the positive direction of x-axis.

(iii) Rotation through an anlge π/4 about the origin in the anticlockwise direction  

(iv) Reflection about x = 0

The final position of the given point is