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$The locus of point of intersection of the line y + m x = \sqrt{a^{2} m^{2} + b^{2}} and m y - x = \sqrt{a^{2} + b^{2} m^{2}} is$

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a

x2+y2=1a2+1b2

b

x2+y2=a2+b2

c

x2−y2=a2−b2

d

1x2+1y2=a2−b2

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detailed solution

Correct option is B

Let the point of intersection of given two lines is P(h, k), which lies on both the lines. ∴ k+mh=a2m2+b2 and mk−h=a2+b2m2Squaring and adding, we get k+mh2+mk-h2=a2m2+b2a2+b2m21+m2k2+1+m2h2=a2m2+b2+a2+b2m2 1+m2k2+h2 =a2m2+1+b2m2+1∴ locus of h,kis x2+y2=a2+b2

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