The locus of the point of intersection of the lines 2 x - y + 4 2 k = 0 and 2 k x + k y - 4 2 = 0 ( k is any…

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
  1. an ellipse whose eccentricity is 13
  2. a hyperbola whose eccentricity is 3
  3. a hyperbola with length of its transverse axis 82
  4. an ellipse with length of its major axis 82

Solution

Given equation of lines are 2x-y+42k=0     ...1

and 2kx+ky-42=0      ...2 

Eliminating k from 1 and 2,

⇒2x+y2x-y-42=42

⇒2x2-y2=-32

⇒y232-x216=1, which is a hyperbola.

⇒e=1+1632=32 and length of transverse axis

=82.

Asked in: JEE Main 2018 (16 Apr Online)

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