Suppose grad … is tangent to the hyperbola … constant in Figure…

Suppose grad $f$ is tangent to the hyperbola $xy=$ constant in Figure C. Draw three level curves of $f(x,y)$. Is $|\text{grad }f|$ larger at $P$ or $Q$? Is $|\text{grad }f|$ constant along the hyperbolas? Choose a function that could be $f$: $x^2+y^2,x^2-y^2,xy,x^2{y}^2$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.4 Directional Derivatives and Gradients, #36