Q. 204.0( 23 Votes )
Find the equation of the normal at the point (am2, am3) for the curve ay2 = x3.
Answer :
It is given that ay2 = x3
Now, differentiating both sides with respect to x, we get
Then, the slope of the tangent to the given curve at (am2, am3) is
Then, slope of normal at (am2, am3)
=
Therefore, equation of the normal at (am2, am3) is given by:
y - am3 =
⇒ 3my – 3am4 = -2x + 2am2
⇒ 2x + 3my – am2(2 + 3m2) = 0
Therefore, equation of the normal at (am2, am3) is 2x + 3my – am2(2 + 3m2) = 0
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