(c) Given curve is x2∕3+y2∕3=a2∕3......(i) Now, let a point on curve P(acos3θ,asin3θ) On differentiating the curve (i) w.r.t x, we get
2
3
x−1∕3+
2
3
y−1∕3
dy
dx
=0⇒
dy
dx
=−(
y
x
)1∕3 ∴ Slope of tangent at point P is m=
dy
dx
|P=−tanθ ∴ Equation of the tangent of the curve at point P is y−asin3θ=−tanθ(x−acos3θ).....(ii) ∵ The tangent (ii) meets the axes at A and B, so A(acosθ,0) and B(0,asinθ) ∴ AB=√a2cos2θ+a2sin2θ=a
