Point Form of Normal:Hyperbola

Q. If a normal drawn at one end of the latus rectum of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ meets the axes at points $A\&B$ respectively, then area of $△OAB$ (in sq.units) is

1. $a^2{e}^5$
2. $\frac{a^2{e}^5}{2}$
3. $\frac{a^2{e}^5}{4}$
4. $\frac{a^2{e}^5}{8}$

Q.

Let P(6, 3) be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If the normal at the point P intersects the X-axis at (9, 0), then the eccentricity of the hyperbola is

1. $\sqrt{\frac{5}{2}}$

2. $\sqrt{\frac{3}{2}}$

3. $\sqrt{2}$

4. $\sqrt{3}$

Q. Let $P(8,4)$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If the normal at point $P$ intersects the $x-$axis at $(12,0)$, then the value of eccentricity is

1. $\sqrt{\frac{7}{2}}$
2. $\sqrt{\frac{3}{2}}$
3. $\sqrt{5}$
4. $\sqrt{3}$

Q. The locus of the middle points of chords of hyperbola $3x^2-2y^2+4x-6y=0$ parallel to $y=2x$ is :

1. $3x-4y=4$
2. $3x+4y=8$
3. $5x-4y=9$
4. $6x-3y=4$

Q.

Let P(6, 3) be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.

If the normal at the point P intersects the x-axis at (9, 0), then the eccentricity of hyperbola is,

1. $\sqrt{\frac{5}{2}}$

2. $\sqrt{\frac{3}{2}}$

3. $\sqrt{2}$

4. $\sqrt{3}$

Q.

Ahyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ is given and a normal is drawn at the point $(5\sqrt{3},4\sqrt{2}).$

What is the abscissa of the point at which it meets the x-axis.

1. 2899

2. $\frac{1911}{25\sqrt{3}}$

3. $\frac{156\sqrt{3}}{5}$

4. $\frac{3150}{\sqrt{3}}$

Q. The equation of the normal to the hyperbola $x^2-9y^2=7$ at the point (4, 1) is .

1. 9x + 4y = 40
2. 9x - 4y = 40
3. 4x + 9y = 40
4. 4x - 9y = 40

Q.

Let P(6, 3) be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$.

If the normal at the point P intersects the x-axis at (9, 0), then the eccentricity of hyperbola is,

1. $\sqrt{\frac{5}{2}}$

2. $\sqrt{\frac{3}{2}}$

3. $\sqrt{2}$

4. $\sqrt{3}$

Q.

Without using Pythagoras theorem, show that $A\left(4,4\right)$, $B\left(3,5\right)$ and $C\left(-1,-1\right)$are the vertices of a right angled triangle.