Example 2. Find the equation of the curve symmetric to the parabola $x^{2}-2 y+3=0$ with respect to $x-y-2=0$.
To solve: In the parabolic equation, by substituting $y+2$, $x-2$ for $x, y$ respectively, we get
$$
y^{2}-2 x+4 y+11=0 \text {. }
$$
(Author's affiliation: Sanhao Middle School, Luwan District, Shanghai)