Q. 223.8( 35 Votes )

# Find the equation

Answer :

The equation of a parabola is y2 = 4ax, then,

On differentiating it with respect to x, we get

2y  Then, the slope of the tangent at (at2, 2at) is Then, the equation of the tangent at (at2, 2at) is given by,

y – 2at = ty -2at2 = x –at2

ty = x + at2

Now, Then, slope of normal at (at2, 2at)

= Then, the equation of the normal at (at2, 2at) is given by:

y – 2at = -t(x-at2)

y – 2at = -tx + at3

y = -tx + 2at + at3

Therefore, the equation of the normal at (at2, 2at) is y = -tx + 2at + at3.

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