Rectangular Car...

If the area of the triangle with vertices (x, 0), (1, 1) and (0, 2) is 4 sq units, then the value of x is

The area enclosed with the curve |x| + |y| = 1 is

The area ( in sq units) of the triangle formed by the lines x = 0, y = 0 and 3x + 4y = 12, is

Three points are A ( 6, 3), B (- 3,5), C (4, -2) and P (x, y) is a point, then the ratio of area of ∆PBC and ∆ ABC is

A variable line passes through a fixed point ( a, ) and meets the coordinate axes in A and B. The locus of the point of intersection of lines through A ,B parallel to coordinate

The equation of the locus of the point of intersection of the straight lines x sin θ + (1 - cos θ) y = a sin θ and x sin θ - (1 + cos θ) y + a sin θ = 0 is

A line segment of 8 units in length moves so that its end points are always on the coordinate axes. Then, the equation of locus of its mid-point is

A variable line through the point (1/5, 1/5) cuts the coordinates axes in the points A and B. If the point P divides AB, internally in the ratio 3 : 1, then the locus of P is

A variable x/a + y/b = 1 is such that a +b = 4. The locus of mind-point of the portion of the line intercepted between the axes is

If a point P(4, 3) is shifted by a distance -√2 unit parallel to the line y = x, then coordinates of P in new position are