# If one of the lines of  $\dpi{100} my^{2}+(1-m^{2})xy-mx^{2}=0$ is a bisector of the angle between the lines $\dpi{100} xy=0,\; \; then \; \; m\; \; is$ Option 1) 1 Option 2) 2 Option 3) –1/2 Option 4) –2

D Divya Saini

As we learnt in

Slope of a line -

If $\Theta$ is the angle at which a straight line is inclined to a positive direction of x-axis, then the slope is defined by

$m= \tan \Theta$.

- wherein

$my^{2}+(1-m)^{2}xy-mx^{2}=0$

$y(my+x)-mx(my+x)=0$

$(y-mx)(my+x)=0$

$xy=0\:\:\:\:is\ x=0 \:\:\:\:and\:\:\:\:y=0$

So slope of line equally inclined is:

$\Theta= \frac{\pi}{4}$

$\tan \Theta=1$

Option 1)

1

This option is correct.

Option 2)

2

This option is incorrect.

Option 3)

–1/2

This option is incorrect.

Option 4)

–2

This option is incorrect.

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