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Ans. (4) 6

Sol. Tangent at $(x_1, y_1)$

$xx_1-2yy_1-4 = 0$

This is parallel to $2x-y = 0$

$\implies{x_1\over2y_1}=2$

$\implies x_1=4y_1\quad$.......(1)

Point $(x_1, y_1)$ lie on hyperbola.

${x_1^2\over4}-{y_1^2\over2}-1=0\quad$.......(2)

On solving eq. (1) and (2)

We get $x_1^2+5y_1^2=6$

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