A straight line `L: 4x-4y+3=0` is rotated in clockwise about the point where the line cuts the y-axis and a circle `S_1` whose centre is `(lambda,3/4)` lambda, | touches both the lines `L and L_1 (L_1` s the line obtained afterrotation) and the x-axis.

Find the length of the chord made by the axis of x, with the circle whose centre is (0,3) and which touches the straight line 3x + 4y = 37.

If the straight line L=3x+4y-k=0 cuts the line segment joining the points P(2,-1) and Q(1,1) in the ratio 4:1 , then the equation of the line parallel to the line y=x and concurrent with the lines PQ and L =0 is

A circle passes through a point (2,8) and touches the lines 4x-3y-24=0 and 4x+3y+42=0 and centre lies on the line x=lambda then (-4 lambda) is

A line L_1=3y-2x-6=0 is rotated about its point of intersection with the y-axis in the clockwise direction to make it L_2 such that the are formed by L_1,L_2 the x-axis, and line x=5 is (49)/3s qdotu n i t s if its point of intersection with x=5 lies below the x-axis. Find the equation of L_2dot

A line L_1-=3y-2x-6=0 is rotated about its point of intersection with the y-axis in the clockwise direction to make it L_2 such that the are formed by L_1,L_2 the x-axis, and line x=5 is (49)/3s qdotu n i t s if its point of intersection with x=5 lies below the x-axis. Find the equation of L_2dot

A line L_1-=3y-2x-6=0 is rotated about its point of intersection with the y-axis in the clockwise direction to make it L_2 such that the are formed by L_1,L_2 the x-axis, and line x=5 is (49)/3s qdotu n i t s if its point of intersection with x=5 lies below the x-axis. Find the equation of L_2dot

A circle touches both the x-axis and the line 4x-3y+4=0 . Its centre is in the third quadrant and lies on the line x-y-1=0 . Find the equation of the circle.

A circle touches both the x-axis and the line 4x-3y+4=0 . Its centre is in the third quadrant and lies on the line x-y-1=0 . Find the equation of the circle.

A line L_(1)-=3y-2x-6=0 is rotated about its point of intersection with the y-axis in the clockwise direction to make it L_(2) such that the are formed by L_(1),L_(2) the x-axis,and line x=5 is (49)/(3) sq.units if its point of intersection with x=5 lies below the x-axis.Find the equation of L_(2).

The centre of the circle whose centre is on the straight line 5x-2y+1=0 and cuts the axis at two points whose abscissae are -5 and 3 is