Question

if x=a cos theta and y=b sin theta, then b square x square+ a square y square?

Answer 1

 b^{2} x^{2} + a^{2} y^{2} , in this equation we substitute the x and y values
hence it becomes b^{2} (a cos \theta )^{2} + a^{2} ( ysin \theta )^{2} 
⇒ b^{2} a ^{2} cos^{2} \theta + a ^{2} b^{2} sin^{2} \theta 
⇒ a^{2} b^{2} cos^{2} \theta + a^{2} b^{2} sin^{2} \theta 
⇒a ^{2} b^{2} ( cos^{2} \theta +sin^{2} \theta )
⇒ a^{2} b^{2}      (as sin^{2} \theta + cos^{2} \theta=1 )

Answer 2

Step-by-step explanation:

substitute values of x and y

b^2(a^2cos^2theta)+a^2(b^2sintheta)

a^2b^2