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

From the equation $$(x - h)^2 + (y - k)^2 = r^2$$ , the center is (h, k).

What is the radius of a circle given its equation?

The radius is the square root of the right side of the equation in standard form. For $$(x - h)^2 + (y - k)^2 = r^2$$ , the radius is $$r = \text{sqrt}(r^2)$$ .

What is the standard form of an ellipse?

The standard form of an ellipse is $$\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$$ , where (h, k) is the center, 'a' is the semi-major axis, and 'b' is the semi-minor axis.

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

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

What is the standard form of a hyperbola?

The standard form of a hyperbola is $$\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$$ or $$\frac{(y - k)^2}{b^2} - \frac{(x - h)^2}{a^2} = 1$$ .

What are the asymptotes of a hyperbola?

The asymptotes are the lines that the hyperbola approaches but never touches. For the hyperbola in standard form, they can be found using the equations derived from the center and the values of 'a' and 'b'.

How do you find the distance between the focus and the vertex of a parabola?

The distance 'p' between the focus and the vertex is determined by the equation $$p = \frac{1}{4|a|}$$ , where 'a' is the coefficient in the parabola's equation.

Conic Sections Flashcards

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FLASHCARD QUESTION

Front

What are conic sections?

Back

Conic sections are the curves obtained by intersecting a plane with a double right circular cone. The four types of conic sections are circles, ellipses, parabolas, and hyperbolas.

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