Question

The transformed equation of $x^{2}+y^{2}=r^{2}$ when the axes are rotated through an angle $36^{\circ}$ is

• A. $\sqrt{5} X^{2}-4 X Y+Y^{2}=r^{2}$
• B. $X^{2}+2 X Y-\sqrt{5} Y^{2}=r^{2}$
• C. $X^{2}-Y^{2}=r^{2}$
• D. $X^{2}+Y^{2}=r^{2}$

Answer 1

Answer: (D)

Given equation is $x^{2}+y^{2}=r^{2} .$ After rotation
$x=X \cos 36^{\circ}-Y \sin 36^{\circ}$
and $y=X \sin 36^{o}+Y \cos 36^{\circ}$
$\therefore X^{2}\left(\cos ^{2} 36^{o}+\sin ^{2} 36^{o}\right)+Y^{2}\left(\sin ^{2} 36^{o}+\cos ^{2} 36^{o}\right)=r^{2}$
$\Rightarrow X^{2}+Y^{2}=r^{2}$