The line x = my + c is normal to x2 = - 4ay , if c is equal to

Question

The line x = my + c is normal to x2 = - 4ay , if c is equal to (A)  - 2 am - m3 a  (B)  - 2 am + am3  (C)  - 2 am - am3  (D)  2 am + am3

Tardigrade Admin · Accepted Answer

We know that equation of normal to the parabola x2=-4 a y in the slope form is x=m y+2 a m+a m3 and point of contact is (2 a m,-a m2) So, line x=m y+c is normal to x2=-4 a y if c=2 a m+a m3

Q. The line $x = m y + c$ is normal to $x^{2} = - 4 a y$ , if $c$ is equal to

$- 2 am - m^{3} a$

$- 2 am + a m^{3}$

$- 2 am - a m^{3}$

$2 am + a m^{3}$

We know that equation of normal to the parabola $x^{2} = - 4 a y$ in the slope form is
$x = m y + 2 am + a m^{3}$
and point of contact is $(2 am, - a m^{2})$
So, line $x = m y + c$ is normal to $x^{2} = - 4 a y$
if $c = 2 am + a m^{3}$

Q. The line x=my+c is normal to x2=−4ay , if c is equal to

−2am−m3a

−2am+am3

−2am−am3

2am+am3