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Hyperbola question

2018 · 16 Apr · Shift 1 · Q47

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JEE Main
Mathematics
Hyperbola
2018 · 16 Apr · Shift 1 · Q47

Hyperbola question

2018 · 16 Apr · Shift 1 · Q47

JEE MainMathematicsHyperbolaMCQ+4 / −1

The locus of the point of intersection of the lines,

\sqrt 2 x - y + 4\sqrt 2 k = 0

and

\sqrt 2 k\,x + k\,y - 4\sqrt 2 = 0

(k is any non-zero real parameter), is :

A
an ellipse whose eccentricity is ${1 \over {\sqrt 3 }}.$
B
an ellipse with length of its major axis $8\sqrt 2 .$
C
a hyperbola whose eccentricity is $\sqrt 3 .$
D
a hyperbola with length of its transverse axis $8\sqrt 2 .$

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