Normal

Q.

Find the equation of the hyperbola satisfying the given conditions.
$\text{foci}(0,\pm \sqrt{10}),\text{passing through (2, 3)}$

Q.

Whats the length of chord intercepted by the parabola $y^2=4xonthelinex+y=0$

1. 

2. 32

3. 

4. 8

Q.

Find the equation of a circle which passes through the origin and cuts off intercepts -2 and 3 from the x-axis and the y-axis respectively.

Q.

Find the equation of the parabola with vertex at the origin, passing through the point $P(3,-4)$ and symmetric about the y-axis.

Q.

Given parabola $y^2=4ax$, find the equation of Normal which will interest the normal at (8, 8) and the parabola at the same point.

1. x + y = 24

2. 2x + y + 24 = 0

3. 2x + y = 24

4. 2x - y = 24

Q. If the line $ax+by=0$ touches the circle $x^2+y^2+2x+4y=0$ and is a normal to the circle $x^2+y^2-4x+2y-3=0,$ then value of $(a,b)$ is/are

1. $(1,2)$
2. $(1,-2)$
3. $(-1,2)$
4. $(-1,-2)$

Q. A straight line $L_1:x-2y+10=0$ meets the circle with equation $x^2+y^2=100$ at $B$ in the first quadrant. If another line $L_2$ through $B$ is perpendicular to $L_1$ and cuts $y-$axis at $P(0,t),$ then the value of $t$ is

Q. The angle between the normals to the parabola $y^2=24x$ at points $(6,12)$ and $(6,-12)$ is :

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$