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Q.

Let C be a curve given by y=1+4x3,x>34. If P is point on C such that the tangent at P has slope 23, then a point through which the normal at P passes, is

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a

(2,3)

b

(1,7)

c

(4,3)

d

(3,4)

answer is B.

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Detailed Solution

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y=1+4x3 dydx=124x34=24x3  Since slope at P=2324x3=23 4x3=9 x=3 y=1+123=4 P=(3,4)
 Slope of normal=32 
Equation of normal at P is 3x+2y=3(3)+2(4) 3x+2y17=0 (1,7) lies on the normal 

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