The locus of point of intersection of the lines `y+mx=sqrt(a^2m^2+b^2)` and `my-x=sqrt(a^2+b^2m^2)` is

Options

A. `x^2+y^2=(1)/(a^2)+(1)/(b^2)`
B. `x^2+y^2=a^2+b^2`
C. `x^2+y^2=a^2-b^2`
D. `1/x^2+1/y^2=a^2-b^2`

Answer

B

Explanation

Let the point of intersection of given two lines be `P(h,k)`, which lies on both the lines.
`therefore k+mh=sqrt(a^2m^2+b^2)`
and `mk-h=sqrt(a^2+b^2m^2)`
Squareing and adding,we get
`(1+m^2)k^2+(1+m^2)h^2=a^2m^2+b^2+a^2+b^2m^2`
Therefore,locus is `x^2+y^2=a^2+b^2`.