1.9.16 Implicit differentiation (A-level only)

A magnetic flux contour line $C$ within a specialized superconducting alloy is modeled by the equation

y^2 + 60x - x^2 y = k, \quad y > 0

where $k$ is a constant and $x$ and $y$ represent spatial coordinates measured in micrometers.

Find $dydx\dfrac{dy}{dx}$ in terms of $x$ and $y$ .

[4]

The point $P (p, 10)$ , where $p$ is a constant, lies on $C$ . Given that $P$ is the minimum turning point on $C$ ,

find

(i) the value of $p$

(ii) the value of $k$

[5]

1.9.16 Implicit differentiation (A-level only) Questions