The locus of the point of intersection of the straight lines,
tx−2y−3t=0
x−2ty+3=0 (t R), is :
an ellipse with eccentricity
an ellipse with the length of major axis 6
a hyperbola with eccentricity
a hyperbola with the length of conjugate axis 3
As we learnt in
Locus -
Path followed by a point p(x,y) under given condition (s).
- wherein
It is satisfied by all the points (x,y) on the locus.
Conjugate axis -
The line through the centre and perpendicular to transverse axis.
- wherein
On solving,
Here a=3, b=
Length of conjugrate axis
Option 1)
an ellipse with eccentricity
This option is incorrect
Option 2)
an ellipse with the length of major axis 6
This option is incorrect
Option 3)
a hyperbola with eccentricity
This option is incorrect
Option 4)
a hyperbola with the length of conjugate axis 3
This option is correct
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