# If a normal to the parabola, y²=4x is perpendicular to the line 3y+x+1=0 then the ordinate of the point of intersection of this normal with the directrix of the parabola is?                                      1) -332) 333) 364) -36

Md Mushahid
21 Points
3 years ago
If a normal to the parabola, y²=4x is perpendicular to the line 3y+x+1=0 then the ordinate of the point of intersection of this normal with the directrix of the parabola is?

$y^{2} = 4$ and $a =36$
$y =\pm 6$
$y^{2}= 4x$
differentiate with respect to x
$2y\times y' =4$
$y' =\frac{2}{y}$
$\left ( m \right )_{9,6} =\frac{1}{3}$
slope is at tangent (9,6)
$m'\times m = -1$
$m' =-3$
slope of normal
$y =mx' +c$
$y =-3x +c$
$6 =-3x+c$
$6 =-3\times 9+c$
$c =6+27$
$c =33$
$y = -3x +33$
$3x +y =33$
option B is ans