Given equation of lines are 2x−y+42k=0...(1)and 2kx+ky−42=0...(2)
Eliminating k from (1) and (2),
⇒(2x+y)(−422x−y)=42
⇒2x2−y2=−32
⇒32y2−16x2=1, which is a hyperbola.
⇒e=1+3216=23 and length of transverse axis
=82.
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
Held on 16 Apr 2018 · Verified 6 Jul 2026.
an ellipse whose eccentricity is 31
a hyperbola whose eccentricity is 3
a hyperbola with length of its transverse axis 82
an ellipse with length of its major axis 82
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