Slope Form of Normal : Hyperbola

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

Q.

What will be the value of ‘p" if the equation of the straight line 3x + 5y = 10 gets changed to 3x + 5y = p after shifting the origin at (2, 2) ?

1. zero

2. 6

3. -6

4. 26

Q. Equation of the diameter of the circle x² + y² − 2x + 4y = 0 which passes through the origin is
(a) x + 2y = 0
(b) x − 2y = 0
(c) 2x + y = 0
(d) 2x − y = 0

Q. For hyperbola $-\frac{x^2}{16}+\frac{y^2}{25}=1$ equation of directrices are

1. $y=\pm \frac{5}{\sqrt{41}}$
2. $y=\pm \frac{25}{\sqrt{41}}$
3. $y=\pm \frac{2}{\sqrt{41}}$
4. $y=\pm \frac{16}{\sqrt{41}}$

Q. At what point of the parabola x² = 9y is the abscissa three times that of ordinate?

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

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