Conic Sections (Foundations)

Core skills for this exam family.

Phase 2 · Gaokao

Conic Sections: core idea

Ellipse

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1

$x^2+y^2=1$ : radius?

Hint: Unit circle. Answer: 1.

1. Circle $(x-2)^2+(y+1)^2=9$ : center $x$ ?
2. Same circle: radius?
3. $y=x^2$ : vertex $y$ ?
4. $y^2=4x$ : focus $x$ -coordinate?
5. $y^2=4x$ : directrix $x=$ ?
6. Ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$ : $a$ ?
7. Hyperbola $\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$ : $a$ ?
8. Circle through origin radius $5$ center origin: equation constant?
9. Identify $xy=1$ : type — enter $1$ hyperbola in rotated axes sense / rectangular. Use $1$ .