Find the equation of the ellipse that passes through the origin and has the foci at the points `(-1, 1) and S\'(1,1)`.

Find the equation of the cure which passes through the origin and has the slope x+3y-1 at the point (x,y) on it.

Find the equation of the ellipse which passes through the points (3,1) and (2,2).

Find the vector and cartesian equations of the line that passes through : (i) the origin and (5, -2, 3) (ii) the points (1,2,3) and (2,-1,4)

Find the equation of the line passing through the point (2,1) and (-2,4).

Find the equation of the ellipse having axes long the coordinate axes and passing through the points (4, 3) and (-1, 4) .

The equation of the ellipse whose centre is at origin and which passes through the points (-3,1) and (2,-2) is

Find the equation of a circle passes through the point (1,-1) and whose centre is at origin.

Find the equation of a line passing through origin and parallel to the line joining the points (1,3) and (2,-1) .

The equation of the circle passing through the point (1,1)