Question

$x=a\cos \theta +b\sin \theta ;y=a\sin \theta -b\cos \theta$ is circle whose equation is

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

Answer 1

The correct option is B $x^2+y^2=a^2+b^2$

$x^2=a^{2}co{s}^2\theta +b^{2}si{n}^2\theta +2absin\theta cos\theta$

$y^2=a^{2}si{n}^2\theta +b^{2}co{s}^2\theta -2absin\theta cos\theta$

$ASsi{n}^2\theta +co{s}^2\theta =1$

$\Rightarrow x^2+y^2=a^2+b^2\Rightarrow \left(B\right)$