A line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line `x+y=0` which lies in the second quadrant. Then the locus of the midpoint of the line has equation.

A rod of length l slides with its ends on two perpendicular lines. Find the locus of its midpoint.

Find the equation of a circle which touches both the axes and the line 3x-4y+8=0 and which lies in the third quadrant.

A straight line through the point of intersection of the lines x+2y = 4 and 2x +y =4 meets the coordinates axes at A and B. The locus of the midpoint of AB is

A line of fixed length a+b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of the point which divides this line into portions of length aa n db is (a) an ellipse (b) parabola (c) straight line (d) none of these

A straight line segment AB of length 'a' moves with its ends on the axes. Then the locus of the point P which divides the line in the ratio 1:2 is

The ends A and B of a rod AB of length 8 unit slide along the lines y=2 and x=4 respectively. Find the equation to the locus of the mid point of the rod.

A straight line through the point of intersection of the lines x + 2y = 4 and 2 x + y = 4 meets the coordinate axes at A and B .the locus of the midpoint of AB is _

Let A be any variable point on the X-axis and B the point (2,3). The perpendicular at A to the line AB meets the Y-axis at C. Then the locus of the mid-point of the segment AC as A moves is given by the equation

Let AB be a line segment of length 4 unit with the point A on the line y=2x and B on the line y=x. Then locus of middle point of all such line segment is

The end points P and Q of a rod PQ having length 8 unit slide along the lines y = 2 and x = 4 respectively. Find the equation of the locus of the mid point of the rod.