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Question

If the curve ay+x2=7, and x3=y cut orthogonally at 1,1, then the value of a is


A

1

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B

0

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C

6

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D

6

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Solution

The correct option is C

6


Step 1: Find the slope dydx at any point on given curves

Equation of the curve are

ay+x2=7 ...........................(1)

x3=y ...........................(2)

Differentiating the equation (1) with respect to x

adydx+2x=0dydx=-2xam1=-2xa

Differentiating the equation (2) with respect to x

3x2=dydxm2=3x2

Step 2: Apply condition of orthogonality and solve equation to find a

Curves cuts orthogonally

m1×m2=-1-2xa×3x2=-16x3a=16x3=a

Since 1,1 is the point of intersection of two curves

Put x=1

a=6·13a=6

Hence, a=6, so, the correct option is (C).


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