How the equation is transformed when origin is changed and axes is rotated ?

The point (4,3) when the axes translated to the point (3,1) and then axes are rotated through 30^(@) about the origin,then the new position of the point is

The equation xy-x+2y-6=0 transforms as XY=C , when the origin is shifted to a suitable point (h,k) , then, 5h+k=?

A transformer changes the voltage

If the transformed equation of a curve when the origin is translated to (1,1) is X_( riginal )^(2)+2X-Y+2=0 then the original equation of the curve is

Find the equation to which the equation x^(2)+7xy-2y^(2)+17x-26y-60=0 is transformed if the origin is shifted to the point (2,-3), the axes remaining parallel to the original axies.

Find the equation to the ellipses,whose centres are the origin,whose axes are the axes of coordinates,and which pass through

The co-ordinate axes are rotated about the origin O in the counter-clockwise direction through an angle 60^(@) If a and b are the intercepts made on the new axes by a straight line whose equation referred to the original axes is 3x + 4y = 5 , then (1)/(a^(2)) + (1)/(b^(2)) =