How do you find the foci of an ellipse given by the equation $$\frac{x^2}{25} + \frac{y^2}{9} = 1$$ ?

The foci are found using the formula c = $$\text{sqrt}(a^2 - b^2)$$ , where a^2 = 25 and b^2 = 9. Thus, the foci are (±√16, 0) or (±4, 0).

What is the relationship between the lengths of the axes and the foci in an ellipse?

In an ellipse, the distance to the foci (c) is given by $$c = \text{sqrt}(a^2 - b^2)$$ , where a is the semi-major axis and b is the semi-minor axis.

What is the equation of a circle in standard form?

The equation of a circle in standard form is $$(x-h)^2 + (y-k)^2 = r^2$$ , where (h, k) is the center and r is the radius.

What is the definition of a conic section?

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

What is the difference between a major axis and a minor axis in an ellipse?

The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter, perpendicular to the major axis.

What is the formula for the area of an ellipse?

The area of an ellipse is given by the formula $$A = \text{π}ab$$ , where a and b are the lengths of the semi-major and semi-minor axes.

What is the definition of the directrix of a hyperbola?

The directrix of a hyperbola is a line used in the definition of the hyperbola, where the distance from any point on the hyperbola to a focus divided by the distance to the directrix is a constant greater than 1.

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

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

Pre-Calculus Final: Conic Sections Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the standard form of the equation of an ellipse centered at (h, k)?

Back

2.

FLASHCARD QUESTION

Front

Back

The coordinates of the center are (3, -2).

3.

FLASHCARD QUESTION

Front

Back

The direction of the transverse axis is Vertical.

4.

FLASHCARD QUESTION

Front

What is the standard form of the equation of a hyperbola centered at (h, k)?

Back

5.

FLASHCARD QUESTION

Front

Back

The coordinates of the vertices are (-1, 5) and (-1, 1).

6.

FLASHCARD QUESTION

Front

Which of the following equations represents a hyperbola with vertices at (±4, 0)?

Back

7.

FLASHCARD QUESTION

Front

Back

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