AP Precalculus / Unit 4: Functions Involving Parameters, Vectors, and Matrices
4.6 Conic Sections
Notes
- Parabola: $y=a(x-h)^2+k$ or $x=a(y-k)^2+h$.
- Ellipse: $\displaystyle \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$.
- Hyperbola: $\displaystyle \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$ (or with $y$ first).
Practice
$\displaystyle \frac{x^2}{9}+\frac{y^2}{4}=1$ is a(n):
Sum of squared terms with different denominators.
$\displaystyle \frac{x^2}{16}-\frac{y^2}{9}=1$ is a(n):
Difference of squares.
The ellipse $\displaystyle \frac{x^2}{9}+\frac{y^2}{4}=1$ crosses the $x$-axis at:
$a=3$.
Ready for more? Take the Unit 4 test.