Analytic geometry problems on the gaokao are long but they are made of short, learnable moves. Recognize which move the question is asking for and the problem shrinks.
The first move is always to write the curve in standard form: x²/a² + y²/b² = 1 for an ellipse, x²/a² - y²/b² = 1 for a hyperbola. Identify a, b, and c (with c² = a² ± b²). Half the work of most problems is done here.
For chord-length problems, substitute the line into the curve, use Vieta's formulas for x₁+x₂ and x₁x₂, then apply the chord-length formula |AB| = √(1+k²) · |x₁-x₂|. This template solves an enormous fraction of the questions on this topic.
For focus-related questions, the definition (sum or difference of distances to the two foci) is often faster than coordinate bashing. When the question mentions a focus, always try the definition first.
Draw the curve. Every time. A sketch of an ellipse takes ten seconds and stops you from writing a hyperbola formula for an ellipse question.