Simplify the equation `x^2 + y^2 + 8x-6y -25=0` to the form `Ax^2 + By^2 = K`, by shifting the origin to a suitable point.

Prove that the equations of the st. lines x+y-1=0 and x-y-1= 0 can be written as x + y = 0 and x-y = 0 by shifting the origin to a suitable point.

Transform the equation x^(2)+y^(2)=ax into polar form.

The equation x+2y=3,y-2x=1 and 7x-6y+a=0 are consistent for

If the equation of a circle is: x^2 + y^2 + 8x -10y+8=0 , then its centre is :

Find the equation of the image of the circle : x^2 + y^2 + 8x-16y + 64=0 in the mirror x = 0.

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

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 equation of the normals to the circle x^2+y^2-8x-2y+12=0 at the point whose ordinate is -1

What does the equation (a-b)(x^2+y^2)-2a b x=0 become if the origin is shifted to the point ((a b)/(a-b),\ 0) without rotation?

Find the equation of the circle concentric with the circle x^2 + y^2+4x+ 6y+11=0 and Passing through the point (5, 4).