What is the equation of a circle with center (0, 0) and radius 5?

The equation of the circle is $$x^2 + y^2 = 25$$ .

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

To convert the general form $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ to standard form, complete the square for x and y.

What is the significance of the values a and b in the ellipse equation?

The values a and b determine the shape and size of the ellipse; a is the distance from the center to the vertices along the major axis, and b is the distance to the vertices along the minor axis.

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

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

How do you find the coordinates of the foci of an ellipse?

The coordinates of the foci of an ellipse centered at (h, k) are given by (h ± c, k), where c = $$\text{sqrt}(a^2 - b^2)$$ .

What is the relationship between the semi-major axis and the semi-minor axis in an ellipse?

In an ellipse, the semi-major axis (a) is always greater than or equal to the semi-minor axis (b), i.e., $$a ≥ b$$ .

Identify the center and radius of the circle given by the equation $$(x - 1)^2 + (y + 4)^2 = 36$$ .

Center: (1, -4), Radius: 6 units.

What is the equation of an ellipse with a horizontal major axis?

The equation of an ellipse with a horizontal major axis is $$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$$ .

Ellipse and Circle TOTD Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard form of the equation of an ellipse?

Back

2.

FLASHCARD QUESTION

Front

How do you find the center of a circle given its equation?

Back

3.

FLASHCARD QUESTION

Front

What do the variables a and b represent in the equation of an ellipse?

Back

In the equation of an ellipse, a represents the length of the semi-major axis, and b represents the length of the semi-minor axis.

4.

FLASHCARD QUESTION

Front

What is the relationship between the center and the radius in the equation of a circle?

Back

5.

FLASHCARD QUESTION

Front

Back

Center: (-3, 2), Radius: 4 units.

6.

FLASHCARD QUESTION

Front

What is the formula to calculate the distance between the foci of an ellipse?

Back

7.

FLASHCARD QUESTION

Front

How do you determine if a given point lies inside, outside, or on a circle?

Back

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