UPSC NDA Math Model Paper 10

Given curves are y−ax3=4 and x2=y
slope of tangent of the curve y−ax3=4 is m1=

dy

dx

=3x2a
⇒ slope of tangent of the curve y−ax3=4 at the point (−1,1) is m1=3a .
Now, slope of tangent of the curve x2=y is m2=

dy

dx

=2x
⇒ slope of tangent of the curve x2=y at the point (−1,1) is m2=−2
Given, the curve y−ax3=4 and x2=y, cut orthogonally at (−1,1)
⇒m1.m2=−1
⇒(3a)(−2)=−1
⇒a=

1

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