Slope Form of Normal : Hyperbola

Q. $\mathrm{The}\mathrm{equation}\left(s\right)\mathrm{of}\mathrm{the}\mathrm{normal}\left(s\right)\mathrm{to}\mathrm{the}\mathrm{hyperbola}$ $3x^2-y^2=1\mathrm{having}\mathrm{slope}\frac{1}{3}$ $\mathrm{is}/\mathrm{are}:$

1. $\sqrt{2}(x-3y)=4$
2. $\sqrt{2}(x-3y)=-4$
3. $\sqrt{2}(x-3y)=8$
4. $\sqrt{2}(x-3y)=-8$

Q. $\mathrm{The}\mathrm{equation}\left(s\right)\mathrm{of}\mathrm{the}\mathrm{normal}\left(s\right)\mathrm{to}\mathrm{the}\mathrm{hyperbola}$ $3x^2-y^2=1\mathrm{having}\mathrm{slope}\frac{1}{3}$ $\mathrm{is}/\mathrm{are}:$

1. $\sqrt{2}(x-3y)=4$
2. $\sqrt{2}(x-3y)=-4$
3. $\sqrt{2}(x-3y)=8$
4. $\sqrt{2}(x-3y)=-8$

Q.

The equation of the normal of slope m to the hyperbola
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
is given by $y=mx\pm \frac{m(a^2+b^2)}{\sqrt{a^2-b^2{m}^2}}$

1. False

2. True

Q.

The equation of the normal of slope m to the hyperbola
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
is given by $y=mx\pm \frac{m(a^2+b^2)}{\sqrt{a^2-b^2{m}^2}}$

1. True

2. False