Question

If $x=5\cos \theta$ and $y=5\sin \theta ,$ then $x^2+y^2=$

• A. 5
• B. 1
• C. 25
• D. 125

Answer 1

The correct option is C 25

We know that ${\cos }^2\theta +{\sin }^2\theta =1$

$\therefore x^2+y^2=\left(5\cos \theta {)}^2\right(5{\sin }^2\theta {)}^2$

$⟹x^2+y^2=25{\cos }^2\theta +25{\sin }^2\theta$

$⟹x^2+y^2=25({\cos }^2\theta +{\sin }^2\theta )$

$⟹x^2+y^2=25\left(1\right)$

$⟹x^2+y^2=25$