Question

(i) $x=asin\theta -bcos\theta$
$y=acos\theta +bsin\theta$

• A. $x^2+y^2=a^2+b^2$
• B. $x^2+y^2=a^2$
• C. $x^2{y}^2=a^2+b^2$
• D. $x^2-y^2=a^2+b^2$

Answer 1

Answer: (A)

$x^2+y^2=a^2+b^2$

$x^2+y^2=(a\sin \theta -b\cos \theta {)}^2+(a\cos \theta +b\sin \theta {)}^2$

$=a^2{\sin }^2\theta +b^2{\cos }^2\theta -2ab\sin \theta \cos \theta +a^2{\cos }^2\theta +b^2{\sin }^2\theta +2ab\sin \theta \cos \theta$

$x^2+y^2=a^2+b^2$.