Equation of Normal When Slope Is Given

Q.

The point on the curve $\sqrt{x}+\sqrt{y}=\sqrt{a}$ the normal at which is parallel to the $x-$axis is

1. $(0,0)$

2. $(0,a)$

3. $(a,0)$

4. $(a,a)$

Q. Let L be a normal to the parabola $y^2=4x$. If L passes through the point (9, 6), then L is given by

1. $y-x+3=0$
2. $y+3x-33=0$
3. $y+x-15=0$
4. $y-2x+12=0$

Q. The equation of the normals at the end points of the latus rectum of the parabola $y^2=8x$ is/are

1. $x+y+6=0$
2. $x-y+6=0$
3. $x-y-6=0$
4. $x+y-6=0$

Q. The equation of the line of the shortest distance between the parabola $y^2=4x$ and the circle $x^2+y^2-4x-2y+4=0$

1. x+y=3
2. x-y=3
3. 2x+y=5
4. done

Q.

Find the equation of normal having slope 1 to the parabola
$y^2=4x$

1. $y=x-3$

2. $y=x+3$

3. $y=x$

4. $y=2x-3$

Q. The equation of the line of the shortest distance between the parabola $y^2=4x$ and the circle $x^2+y^2-4x-2y+4=0$

1. x+y=3
2. x-y=3
3. 2x+y=5
4. done

Q. If the normal at the point $P(a{p}^2,2ap)$ meets the parabola at $Q(a{q}^2,2aq)$ such that the lines joining the origin to $P$ and $Q$ are at right angle, then

1. $p^2=2$
2. $pq-4=0$
3. $pq+4=0$
4. $p^2=4$

Q. The line y = 2x + k is a normal to the parabola $y^2=4x$ then k =

1. 12
2. -12
3. 10
4. -10

Q.

Given slope m, find the equation of normal having slope m to the parabola $y^2=4ax$

1. $y=mx+2am-a{m}^3$

2. $y=mx-2am-a{m}^3$

3. $y=mx-2am-m^3$

4. $y=mx-2am+a{m}^3$

Q. The line $x+2y=36$ is normal to the parabola $x^2=12y$ at the point whose distance from the focus of the parabola is