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Question

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


A

12,12

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B

12,-13

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C

12,13

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D

-12,-12

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Solution

The correct option is A

12,12


Explanation for the correct answer

Given curve, y(x2)(x3)=x+6

Substitute x=0 to find intersection of curve with y axis.

y-2-3=6

y=1

The intersection of the curve with y axis is at x=0,y=1

Differentiating with respect to x

dydxx-2x-3+y2x-5=1

Substitute x=0,y=1 to obtain the value of slope at the intersection of the curve and y axis

dydx-2-3+1-5=1

dydx=1

Tangent is perpendicular to the normal.

Hence the slope of the normal is -1.

The equation for the normal is given by using the slope point form of a line

y-1=-1(x-0)

x+y-1=0

From the given options 12,12 lies on the normal x+y-1=0

Hence, option A is the right answer.


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