If the origin is shifted to `(h,k)` and the axes are rotated through an angle `theta` ,then the co-ordinates of a point `P(x,y)` are transformed as `P(X,Y)=`

If the axes are rotated through an angle theta then the co-ordinates of a point P(x,y) are transformed as P'(X,Y) then X=,Y=

If the origin is shifted to (1,-2) and axis are rotated through an angle of 30^(@) the co- ordinate of (1,1) in the new position are

If the origin is shifted to (h,k) by translation of axes . then the Co-ordinates of a point P(x,y) are transformed as P(x', y') = O P(x+h, y+k) O P(x-h, y-k) O P(x'– h, y' - k) O P(x' – h, y' +k)

If the origin is shifted to (h,k) ,the coordinates of a point P(x,y) transformed to P(X,Y) then new co-ordinates are

If the axes are rotated through an angle theta without changing the position of the origin,then the transformation is called.

If the origin is shifted to the point O(2,3) the axes remaining parallel to the original axes the new co-ordinate of the point A (1,3) is ….

When the origin is shifted to a point P, the point (2,0) is transformed to (0,4) then the coordinates of P are

When the origin is shifted to a point P, the point (2,0) is transformed to (0,4) then the coordinates of P are

The co-ordinates of a point P referred to a rectangular co-ordinate system where O is the origin are (1,-2). The axes are rotated about O through an angle theta. If the co-ordinates of P in the new system are (k-1,k+1), then k^(2) is equal

Let P(x, y) be a variable point such that |sqrt((x-1)^(2)+(y-2)^(2))-sqrt((x-5)^(2)+(y-5)^(2))=4 which represents a hyperbola. Q. If origin is shifted to point (3, (7)/(2)) and axes are rotated in anticlockwise through an angle theta , so that the equation of hyperbola reduces to its standard form (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , then theta equals