What is the definition of eccentricity in conic sections?

Eccentricity is a measure of how much a conic section deviates from being circular; it is defined as $$e = \frac{c}{a}$$ for ellipses and hyperbolas.

What is the equation for an ellipse in standard form?

The standard form is $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ .

What is the focus of a parabola?

The focus is a point from which distances to points on the parabola are measured.

What is the directrix of a parabola?

The directrix is a line used in the definition of a parabola, where each point on the parabola is equidistant from the focus and the directrix.

What is the equation for a hyperbola that opens left and right?

The equation is $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ .

What is the polar coordinate representation of the point (3, 3π/4)?

In polar coordinates, the point is represented as (r, θ) = (3, 3π/4).

What is the relationship between the foci and vertices of a hyperbola?

The distance from the center to each focus is c, and the distance from the center to each vertex is a, where c^2 = a^2 + b^2.

What is the equation for a circle in polar coordinates?

The equation is $$r = a$$ , where a is the radius.

Exploring Conic Sections and Polar Equations Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the equation for a polar graph that represents a circle with a radius of 3?

Back

Tags

CCSS.HSN.CN.B.4

2.

FLASHCARD QUESTION

Front

What is the standard form of a hyperbola?

Back

3.

FLASHCARD QUESTION

Front

Back

This equation represents a hyperbola.

4.

FLASHCARD QUESTION

Front

What is the general form of a conic section?

Back

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

What is the equation for a parabola that opens upwards?

Back

Tags

CCSS.HSF-IF.C.7A

6.

FLASHCARD QUESTION

Front

What is the difference between an ellipse and a circle?

Back

A circle is a special case of an ellipse where the two foci coincide and the major and minor axes are equal.

7.

FLASHCARD QUESTION

Front

What is the polar equation for a lemniscate?

Back

Tags

CCSS.HSF-IF.C.7D

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