Find the transformed equation of the curve. `x^2 + y^2 + 4x - 6y + 6 = 0`, when the origin is shifted to the point (-2,3).

Find the transformed equation of the curve : x^2+y^2+4x-6y+16=0 when the origin is shifted to the point (-2,3).

Find the transformed equation of the curve : y^2-4x + 4y +8 =0 , when the origin is shifted to (1, -2).

Find the transformed equation of the st. line 2x-3y + 5 = 0 when the origin is shifted to the point (3, -1) after translation of axes.

Find the parametric equation of the circles : 3x^2 + 3y^2+4x-6y-4=0 .

Find the equation of the curve 2x^(2)+y^(2)-3x+5y-8=0 when the origin is transferred to the point (-1, 2) without changing the direction of axes.

Find the transformed equations of the following when the origin is shifted to the point (1, 1) by a translation of axes : xy-y^2-x +y=0 .

Find the transformed equations of the following when the origin is shifted to the point (1, 1) by a translation of axes : x^2-y^2 - 2x+ 2y = 0 .

Find the equations of normal(s) to the curve x^2 + 2y^2 - 4x - 6y + 8 = 0 at the point(s) whose absscissa is 2.

Find the angle of intersection of the curves: x^2+y^2-4x-1=0 and x^2+y^2 - 2y - 9 =0

Prove that the curves y^2 = 4x and x^2 + y^2 - 6x + 1 = 0 touch each other at the point (1,2)