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Q. The normal to the curve y(x2)(x3)=x+6 at the point where the curve intersects the y-axis passes through the point :

JEE MainJEE Main 2017Application of Derivatives

Solution:

y(x2)(x3)=x+6
At y-axis, x=0,y=1
Now, on differentiation.
dydx(x2)(x3)+y(2x5)=1
dydx(6)+1(5)=1
dydx=66=1
Now slope of normal =1
Equation of normal y1=(x0)
y+x1=0... (i)
Line(i) passes through (12,12)