A circle passes through (2,1) and x + 2y =1 is a tangent to it at (3, -1) .Find its equation.

A circle passes through the points (3, 4), (-1, 2) and its radius is 5 unit, find the equation of the circle.

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 a curve passing through (1,1) and whose slope of tangent at a point (x, y) is -(x)/(y) .

Find the equation of a curve passing through (1,1) and whose slope of tangent at a point (x, y) is -(x)/(y) .

Find the equation of the circle passing through the point (1, -2) and having its centre at the point of intersection of lines 2x-y+3=0 and x+2y-1=0.

Find the equation of the circle passing through the point (-1,3) and having its centre at the point of intersection of the lines x-2y=4 and 2x+5y+1=0

3x + y = 5 and x+y+1 = 0 are two diameters to the circle which passes through the point (-2, 2). Find its equation. Also find the radius of the circle.

Solve the following: A line is perpendicular to the line 3x+2y-1=0 and passes through the point A(1,1) .Find its equation

A circle passes through the point of intersection of the circles x ^2 + y ^2 + 13x - 3y = 0 and 2x ^2 + 2y ^2 + 4x - 7y - 25 = 0 and also through the point (1, 1). Find its equation.