What is the equation of an ellipse centered at the origin with a semi-major axis of 5 and a semi-minor axis of 3?

The equation of the ellipse is $$\frac{x^2}{3^2} + \frac{y^2}{5^2} = 1$$ .

What is the distance formula used to find the distance between two points (x1, y1) and (x2, y2)?

The distance formula is $$d = \text{sqrt}((x2 - x1)^2 + (y2 - y1)^2)$$ .

What is the general form of the equation of a circle?

The general form of the equation of a circle is $$x^2 + y^2 + Dx + Ey + F = 0$$ .

How do you convert the general form of a circle's equation to standard form?

To convert to standard form, complete the square for the x and y terms.

What is the relationship between the axes of an ellipse and its equation?

The lengths of the semi-major and semi-minor axes correspond to the denominators in the ellipse's equation in standard form.

What is the equation of a circle with a diameter from (1, 2) to (5, 6)?

The equation of the circle is $$(x - 3)^2 + (y - 4)^2 = 8$$ .

What are the coordinates of the center of the ellipse given by the equation $$\frac{(x-4)^2}{16} + \frac{(y+1)^2}{9} = 1$$ ?

The center of the ellipse is (4, -1).

What is the formula for the area of an ellipse?

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

Equations of Circles and Ellipses Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard form of the equation of a circle?

Back

2.

FLASHCARD QUESTION

Front

How do you determine if an ellipse is vertical or horizontal?

Back

3.

FLASHCARD QUESTION

Front

Back

The center of the circle is (-2, 3).

4.

FLASHCARD QUESTION

Front

Back

The radius of the circle is 5.

5.

FLASHCARD QUESTION

Front

Back

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

6.

FLASHCARD QUESTION

Front

What is the equation of a circle with center (3, -2) and radius 4?

Back

7.

FLASHCARD QUESTION

Front

How do you find the foci of an ellipse?

Back

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