Question

The transformed equation of $xcos\alpha +ysin\alpha =P$ when the axes are rotated through an angle $\alpha$ is

• A. $X=P$
• B. $X+P=0$
• C. $Y=P$
• D. $Y+P=0$

Answer 1

Answer: (A)

$X=P$

By rotation of axes,
$x=x_1\cos \alpha -y_1\sin \alpha$
$y=x_1\sin \alpha +y_1\cos \alpha$
$x\cos \alpha +y\sin \alpha =P$..........(given)
$\Rightarrow x_1({\cos }^2\alpha +{\sin }^2\alpha )+y(\sin \alpha \cos \alpha -\cos \alpha \sin \alpha )=P$..............(substitute the values of x and y)
$x_1=P$ => X=P.