Question

For all values of $\theta$, the locus of the point of intersection of the lines $xcos\theta +ysin\theta =a$ and $xsin\theta -ycos\theta =b$ is

• A. An ellipse
• B. A circle
• C. A parabola
• D. A hyperbola

Answer 1

The correct option is B A circle

The point of intersection is $x=acos\theta +bsin\theta$
$y=asin\theta -bcos\theta$.
Therefore, $x^2+y^2=a^2+b^2$.
Obviously, it is equation of a circle.