A Circle is drawn with its centre on the line `x+y=2` to touch the line `4x - 3y +4=0` and pass throughthe point `(0, 1)`. Find its equation.

A circle whose centre is the point of intersection of the lines 2x-3y+4=0\ a n d\ 3x+4y-5=0 passes through the origin. Find its equation.

A circle whose centre is the point of intersection of the lines 2x-3y+4=0 and 3x=4y-5=0 passes through the origin.Find its equation.

(i) A circle whoe centre is the point of intersection of the line 2x - 3y + 4 - 0 and 3x + 4y - 5 = 0 passes through the origin. Find its equation. (ii) Find the equation of the circle passing through the point (1,-1) and centre at the intersection of the lines (x -y) = 4 and 2x + 3y = -7.

A circle passes through the point (-2, 1) and touches the straight line 3x - 2y = 6 at the point (4, 3) . Find its equation.

Find the equation of the line drawn through the point of intersection of the lines x-2y+3=0 and 2x-3y+ 4=0 and passing through the point (4,-5).

A circle with its centre on the line y=x+1 is drawn to pass through the origin and touch the line y=x+2 .The centre of the circle is

Find the equation of the circle with centre on the line 2x + y = 0 and touching the line 4x - 3y + 10-0, 4x - 3y = 30 .

Find the equation of the circle with centre on the line 2x + y = 0 and touching the line 4x - 3y + 10-0, 4x - 3y = 30 .

A line parallel to the line x-3y=2 touches the circle x^(2)+y^(2)-4x+2y-5=0 at the point

The equation of the circle having its centre on the line x +2y - 3 = 0 and passing through the points of intersection of the circles x^2 + y^2 - 2x - 4y +1 = 0 and x^2+y^2 -4x -2y +4=0 is :