Fix the mistake: Conic Sections (Parabolas, Ellipses, and Hyperbolas)
Conic Sections ① Parabola
Parabola: The locus of points equidistant from a fixed point F (the focus) and a fixed line l (the directrix).
Standard form y² = 4px (p>0):
・Focus F(p, 0) ・Directrix x = −p
Example ① Find the focus and directrix of y² = 8x.
Solution:4p = 8 → p = 2。Focus (2,0), directrix x = −2
Solution:4p = 8 → p = 2。Focus (2,0), directrix x = −2
Key Point
- When the axis is the y-axis: x² = 4py, focus (0,p), directrix y = −p
Practice Problems
- Find the focus and directrix of x² = 12y.
Answers and Explanations
- Answer:Focus (0, 3), directrix y = −3
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