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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) -33 2) 33 3) 36 4) -36

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) -33
2) 33
3) 36
4) -36

Grade:12th pass

1 Answers

Md Mushahid
21 Points
2 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 

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