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IMG_20190218_073647.jpg 3. The locus of the point of intersection of the lines, y + 4Ck = 0 and •Ek-r + ky — 4.15k = 0 (k is any non-zero real parameter), is: (a) an ellipse whose eccentricity is — . (b) an ellipse with length of its major axis 8vlä (c) a hyperbola whose eccentricity is (d) a hyperbola with length Of its transverse axis 2.

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\sqrt2x-y= -4\sqrt2k

k(\sqrt2x+y)= 4\sqrt2

also (\sqrt2x+y)(\sqrt2x-y)= -16\cdot 2

2x^{2}-y^{2}=-32

\frac{y^{2}}{32}-\frac{x^{2}}{16}=1

this is hyperbola  a^{2}=32 \Rightarrow a=4\sqrt2

transverse  axis = 2a = 8\sqrt2

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himanshu.meshram

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