Question

For all values of $\theta$, the locus of the point of intersection of the lines $x \cos \theta + y \sin \theta = a$ and $x \sin \theta - y \cos \theta = b$ is.

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

Answer 1

Answer: (B)

A circle

Answer 2

The point of intersection is

$x = a \cos \theta + b \sin \theta$

$y = a \sin \theta - b \cos \theta$.

Therefore,$x ^ { 2 } + y ^ { 2 } = a ^ { 2 } + b ^ { 2 }$.

Obviously, it is equation of a circle.