11.22 Eliminate $t$ from the equations $x=10^{\cos t}, y=10^{\sin t}$.
11.22 By logarithmizing the equalities with base 10, we get $\lg x=\cos t, \lg y=\sin t$. Then

$$
\cos ^{2} t+\sin ^{2} t=\lg ^{2} x+\lg ^{2} y, \text { or } \lg ^{2} x+\lg ^{2} y=1
$$