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Q.
The locus of point of intersection of the line $y+m x=$ $\sqrt{a^{2} m^{2}+b^{2}}$ and $m y-x=\sqrt{a^{2}+b^{2} m^{2}}$ is
Straight Lines
Solution:
Let the point of intersection of given two lines is $P(h, k)$, which lies on both the lines.
$\therefore k+m h=\sqrt{a^{2} m^{2}+b^{2}}$
and $m k-h=\sqrt{a^{2}+b^{2} m^{2}}$
Squaring and adding, we get
$\left(1+m^{2}\right) k^{2}+\left(1+m^{2}\right) h^{2}=a^{2} m^{2}+b^{2}+a^{2}+b^{2} m^{2} $
$\therefore $ locus is $ x^{2}+y^{2}=a^{2}+b^{2}$