Question

Locus of the point of intersection of lines $x\cos \alpha +y\sin \alpha =a$ and $x\sin \alpha -y\cos \alpha =a$ ($\alpha ϵR$) is ?

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

Answer 1

The correct option is A $x^2+y^2=a^2$

Let P(h, k) be the point of intersection of the given lines.

Then, hcos? + ksin? =a , hsin? kcos? = b

Here a is a variable. So we have to eliminate a.

Squaring and adding (1) and (2),

hcos? + ksin?)² + (hsin? kcos?)² = a² + b²

h² + k² = a² + b²

Hence, locus of (h, k) is x² + y² = a² + b²