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The locus of a point from which 3 normals can be drawn to y2=4x such that the sum of the angles made by them with the axis is 3pie/4 is a a) parabola b) circle c) straight line d) none of these

The locus of a point from which 3 normals can be drawn to y2=4x such that the sum of the angles made by them with the axis is 3pie/4 is a 


a) parabola


b) circle


c) straight line


d) none of these

Grade:

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
12 years ago

Dear student,

Write the equation of normal to parabola.

Normal at the Point (x1, y1 ):

The equation of the tangent at the point (x1, y1) is yy1 = 2a(x + x1). Since the slope of
tangent = 2a/y1 , slope of normal is -y1/ 2a . Also it passes through (x1, y1).

Hence its equation is y - y1 = y1 / 2a ( x - x1 )                          . . . . .   (i)

 

Normal in Terms of m:

In equation (i), put - y1 / 2a = m so that y1 = -2am and x1 = y12 / 4a = am2, then the equation becomes

 y = mx - 2am - am3                                                     . . . . .  (ii)

where m is a parameter. Equation (ii) is the normal at the point (am2, -2am) of the parabola.

 

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All the best.

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Sagar Singh

B.Tech, IIT Delhi

sagarsingh24.iitd@gmail.com

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