Question

The line `lx+my+n=0` is a normal to the parabola `y^2 = 4ax` if
A. `al(l^(2)+2m^(2))+m^(2)n=0`
B. `al(l^(2)+2m^(2))+m^(2)n`
C. `al(2l^(2)+2m^(2))+m^(2)n=0`
D. `al(2l^(2)+2m^(2))+m^(2)n`

Answer 1

Correct Answer - A
The equation of the line is lx+n=0.
`or, y=((-1)/m)x+((-n)/m)`
This will be normal to `y^(2)=4ax`, if
`(-n)/m=-2a((-1)/m)-a((-1)/m)^(3)" "{"Using : c"=-2am-am^(3)}`
`rArr" "-nm^(2)=2alm^(2)+al^(3)rArral(l^(2)+2m^(2))+m^(2)n=0`