Conic sections are curves formed by the intersection of a plane and a double-napped cone. The four main types of conic sections are circles, ellipses, parabolas, and hyperbolas. Each type can be represented by a specific equation and has unique properties that define its shape and characteristics. Understanding how to identify and manipulate these equations is a key skill in Algebra 2. This worksheet will provide a hands-on way to practice identifying and understanding these fundamental concepts.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Circle | a. The set of all points equidistant from a fixed point (focus) and a fixed line (directrix). |
| 2. Ellipse | b. The set of all points such that the sum of the distances to two fixed points (foci) is constant. |
| 3. Parabola | c. The set of all points equidistant from a center point. |
| 4. Hyperbola | d. The set of all points such that the absolute difference of the distances to two fixed points (foci) is constant. |
| 5. Focus | e. A fixed point used in the definition of conic sections. |
Answers:
Complete the following paragraph with the correct terms:
A _______ is a conic section formed when a plane intersects a cone parallel to its side. The standard form equation of a circle centered at (h,k) with radius r is $(x-h)^2 + (y-k)^2 = r^2$. An _______ has two axes: the major axis and the minor axis. A _______ has two branches and asymptotes. The general form of a conic section can be represented as $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$.
Possible Answers:
Explain how changing the values in the standard form equation of an ellipse, specifically $a$ and $b$ in $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, affects the shape and orientation of the ellipse. Be as specific as possible!
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