Parametric Equation of Normal

Q.

Find the equation of normal to the parabola $y^2=8x$ at (8, 8) using parametric form.

1. 2x + y = 24

2. 2x + y + 24 = 0

3. 2x - y = 24

4. x + y = 24

Q. The two parabolas $y^2=4ax$ and $y^2=4c(x-b)$ cannot have a common normal, other than the axis unless, if

1. $\frac{a-c}{b}>2$
2. $\frac{b}{a-c}>2$
3. $\frac{b}{a}+c>2$
4. $\frac{b}{a-c}<2$

Q. The equation of the locus of the point of intersection of two normals to the parabola $y^2=4ax$ which are perpendicular to each other is

1. $y^2=a(x-3a)$
2. $y^2=a(x+3a)$
3. $y^2=a(x+2a)$
4. $y^2=a(x-2a)$

Q.

Find the equation of normal to the parabola $y^2=4axat(a{t}^2,2at)$ in terms of t, a.

1. $y=tx+a{t}^3+2at$

2. $y=-tx+a{t}^3-2at$

3. $y=-tx+a{t}^3+2at$

4. $y=-tx+a{t}^3+at$

Q. The point of intersection of normals to the parabola $y^2=4x$ at the points whose ordinates are $4$ and $6$ is

1. $(30,-21)$
2. $(21,-30)$
3. $(17,-19)$
4. $(19,-17)$