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Find the equation of the normal to the curve X^3+Y^3=8XY at the point where it is meet by the curve Y^2=4X, other than origin??Ans:Y=X

Find the equation of the normal to the curve X^3+Y^3=8XY at the point where it is meet by the curve Y^2=4X, other than origin??Ans:Y=X

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1 Answers

Khimraj
3007 Points
4 years ago
The meeting point of above two curve are (0,0) and (4,4)
So we have to find out normal to curve x3 + y3 = 8xy at point (4,4)
 differentiating above equation
3x2 +3y2m = 8y +8xm    where m = y’
putting x =4 and y=4
48 + 48m = 32 + 32m
16m = -16
m = -1
slope of normal at (4,4) = -1/m = 1
So equation of normal
(y-4) = 1(x-4)
So y = x.
Hope it clears.

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