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Question

# The locus of the point of intersection of the lines, √2 x−y+4√2 k=0 and √2 kx+ky−4√2=0 (k is any non-zero real parameter), is:

A
an ellipse with length of its major axis 82
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B
a hyperbola with length of its transverse axis 82
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C
a hyperbola whose eccentricity is3
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D
an ellipse whose eccentricity is 13.
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Solution

## The correct option is B a hyperbola with length of its transverse axis 8√2 √2 x−y=−4√2 k............(1)√2 x+y=4√2k............(2)multiplying both equation(√2x+y)(√2x−y−4√2)=4√22x2−y2=−32y232−x216=1Hence, it represents a hyperbolae=√1+1632=√32Also, length of transverse axis = 8√2

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