Question

Find the value of b²x² +a²y²-a²b² , where x=a cos theta and y=b sin theta

Answer 1

I hope this answer is correct

Answer 2

 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 )