Point Form of Normal:Hyperbola

Q.

What is the equation of the normal to the hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ at the point $(5\sqrt{3},2\sqrt{2})$

1. 

2. 

3. 

4. 

Q.

The value of $\lambda$ such that the line joining the origin to the points of the intersection of the line $x+y=1$ and the curve $x^2+y^2+x-2y-\lambda =0$ are mutually perpendicular.

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

2. $\frac{1}{3}$

3. $2$

4. $3$

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.

The focus of the parabola y² - x - 2y + 2 = 0 is

1. 

2. 

3. None of these

4. (1, 1)

Q. The equation of the parabola with focus (0, 0) and directrix x + y = 4 is
(a) x² + y² − 2xy + 8x + 8y − 16 = 0
(b) x² + y² − 2xy + 8x + 8y = 0
(c) x² + y² + 8x + 8y − 16 = 0
(d) x² − y² + 8x + 8y − 16 = 0

Q. 22. An asymptote of a rectangular hyperbola with centre (0, 0) is x+2y=0. The equation of the hyperbola passing through (1, 3) is 1. 2x²–y²+3xy+16=0 2. 2x²–2y²+3xy+7=0 3. 2x²–2y²+xy–9=0 4. 2x²–y²+3xy–2=0

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. If the area bounded by the curves y=kx² and x=ky² is 1 , then find the value of k. (Using integration)

Q.

What is the equation of the normal to the hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ at the point $(5\sqrt{3},2\sqrt{2})$

1. $5\sqrt{2}x+8\sqrt{3}y-41\sqrt{6}=0$

2. $5x+8y-41\sqrt{2}=0$

3. $5\sqrt{3}x+8\sqrt{2}y+41\sqrt{6}=0$

4. $8\sqrt{3}y+5\sqrt{2}y+41\sqrt{6}=0$

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. $\sqrt{3}$