Q.

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

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a

a hyperbola whose eccentricity is  3

b

an ellipse with length of its major axis 82

c

a hyperbola with length of its transverse axis 82

d

an ellise whose eccentricity is 13

answer is D.

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Detailed Solution

Given lines are 2x-y=-42k       k2x+y=42  k=422 x+y     from  &  2x-y=-42422x+y    2x-y 2x+y=-32    2x2-y2=-32    x216-y232=-1 length of transverse axis =232 2b                                              =2×42                                              =82

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