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Question

The locus of the point of intersection of the lines, 2 xy+42 k=0 and 2 kx+ky42=0 (k is any non-zero real parameter), is

A
an ellipse whose eccentricity is 13
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B
a hyperbola whose eccentricity is 3
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C
a hyperbola having length of its transverse axis 82 units
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D
an ellipse having length of its major axis 82 units
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Solution

The correct option is C a hyperbola having length of its transverse axis 82 units
2 xy=42 k .....(1)
2 x+y=42k .....(2)
Multiplying both equation
(2x+y)(2xy42)=42
2x2y2=32
y232x216=1
Hence, it represents a hyperbola having transverse axis along yaxis
e=1+1632=32
Also, length of transverse axis 232= 82 units

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