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=