Question

The locus of the intersection of the lines $x\cos \alpha +y\sin \alpha =a$ and $x\sin \alpha -y\cos \alpha =b$ , where $\alpha$ is variable

• A. $x^2+y^2=a^2+b^2$
• B. $x^2+y^2=b^2$
• C. $x^2+y^2=a^2$
• D. $x^2+y^2=a^2-b^2$

Answer 1

Answer: (A)

$x^2+y^2=a^2+b^2$

Given $x\cos \alpha +y\sin \alpha =a$ and $x\sin \alpha -y\cos \alpha =b$

Squaring and adding both the equation we get,

$x^2+y^2=a^2+b^2$, which is required locus