On shifting the origin to a particular point,the equation `x^(2)+y^(2)-4x-6y-12=0` transforms to `X^(2)+Y^(2)=K` .Then K=

When the origin is shifted to a suitable point, the equation 2x^(2)+y^(2)-4x+4y=0 transformed as 2x^(^^)2+y^^2-8x+8y+18=0^(@) The point to which origin was shifted is

When the axes of coordinates are rotates through an angle pi//4 without shifting the origin, the equation 2x^(2)+2y^(2)+3xy=4 is transformed to the equation 7x^(2)+y^(2)=k where the value of k is

When origin is shifted to the point (4, 5) without changing the direction of the coordinate axes, the equation x^(2)+y^(2)-8x-10y+5=0 is tranformed to the equation x^(2)+y^(2)=K^(2) . Value of |K| is

The origin is shifted to (1,2), the equation y^(2)-8x-4y+12=0 changes to Y^(2)+4aX=0 then a=

When the origin is shifted to (2,3) then the original equation of x^(2)+y^(2)+4x+6y+12=0 is

Find the point to which the origin should be shifted so that the equation y^(2)-6y-4x+13=0 is transformed to the form y^(2)+Ax=0

The equation of the normal at (1,2) to the circle x^(2)-y^(2)-4x-6y-12=0 is

By shifting origin to (-1,2) the equation y^(2)+8x-4y+12=0 changes as Y^(2)=4aX then a=

Shift the origin to a suitable point so that the equation y^(2)+4y+8x-2=0 will not contain term of y and the constant term.