What are the foci of an ellipse?

The foci of an ellipse are two fixed points located along the major axis, at a distance of c from the center, where c = $$\text{sqrt}(a^2 - b^2)$$ .

What is the relationship between the axes of an ellipse?

In an ellipse, the length of the major axis is 2a and the length of the minor axis is 2b, where a > b.

How do you determine the vertex of a parabola from its equation?

The vertex of a parabola given by the equation $$y^2 = 4px$$ is at the origin (0, 0) if not translated. For $$(y - k)^2 = 4p(x - h)$$ , the vertex is at (h, k).

What is the difference between a circle and an ellipse?

A circle is a special case of an ellipse where the lengths of the semi-major and semi-minor axes are equal (a = b).

What is the equation of a hyperbola with a horizontal transverse axis?

The equation of a hyperbola with a horizontal transverse axis is: $$\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$$ .

How do you find the directrix of a parabola given its focus?

If the focus of a parabola is at (p, 0), the directrix is the line $$x = -p$$ .

What is the significance of the eccentricity of a conic section?

The eccentricity (e) of a conic section determines its shape: e = 0 for a circle, 0 1 for a hyperbola.

Review for Conic Sections Flashcards

Student preview

14 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The four types of conic sections are circles, ellipses, parabolas, and hyperbolas.

2.

FLASHCARD QUESTION

Front

What is the standard equation of a circle?

Back

3.

FLASHCARD QUESTION

Front

What is the standard equation of an ellipse?

Back

4.

FLASHCARD QUESTION

Front

What is the standard equation of a hyperbola?

Back

5.

FLASHCARD QUESTION

Front

What is the standard equation of a parabola?

Back

6.

FLASHCARD QUESTION

Front

How do you find the focus of a parabola given its equation?

Back

7.

FLASHCARD QUESTION

Front

What is the definition of the directrix of a parabola?

Back

The directrix of a parabola is a line perpendicular to the axis of symmetry, located at a distance p from the vertex, opposite to the focus.

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