Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+bY^2` where `a,b` are constants such that

Let 0 lt=thetalt=pi/2 and x=X cos theta+Y sin theta, y=X sin theta-Y cos theta such that x^2+2xy+y^2=aX^2+bY^2, where a and b are constant, then

Let 0 lt=thetalt=pi/2 and x=X cos theta+Y sin theta, y=X sin theta-Y cos theta such that x^2+2xy+y^2=aX^2+bY^2, where a and b are constant, then

Let 0 leq theta leq (pi)/(2) and x=X cos theta+Y sin theta y=X sin theta-Y cos theta such that x^(2)+4 x y+y^(2)=a X^(2)+b Y^(2) where a, b are constants, then

Let 0<=theta<=(pi)/(2) and x=X cos theta+Y sin theta,y=X sin theta-Y cos theta such that x^(2)+2xy+y^(2)=aX^(2)+bY^(2), where a and b are constant,then

If x = a cos theta - b sin theta and y = a sin theta + b cos theta, prove that x^2 + y^2 = a^2 + b^2.

If 2y cos theta= xsin theta and 2x sec theta-y cosec theta=3 then x^2/4+y^2=

If x=a cos theta-b sin theta and y=a sin theta+b cos theta then prove that :x^(2)+y^(2)=a^(2)+b^(2)

If 2y cos theta =x sin theta and 2x sec theta -y cosec theta =3, then x ^(2) +4y^(2)=

If xcos theta- y sin theta =a, x sin theta + y cos theta = b , prove that: x^(2) + y^(2) = a^(2) + b^(2) .

If x = X cos theta- Y sin theta, y = X sin theta + Y cos theta and x^2 + 4 x y + y^2 = A X^2 + B Y^2 0 <= theta <= pi/2, then