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 aa) parabolab) circlec) straight lined) none of these

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)

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.