Convert the equation $$y^2 - 18x - 2y + 145 = 0$$ to standard form.

The standard form is $$\left(y-1\right)^2=18\left(x-8\right)$$ .

What is the directrix of the parabola $$(y-k)^2 = 4p(x-h)$$ ?

The directrix is the line $$x = h - p$$ .

What is the definition of a hyperbola?

A hyperbola is a set of all points where the difference of the distances to two fixed points (foci) is constant.

What is the standard form of a hyperbola that opens horizontally?

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

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 of a parabola that opens downward?

The standard form is $$y = -a(x-h)^2 + k$$ .

How do you determine the asymptotes of a hyperbola in standard form?

The asymptotes are given by the equations $$y - k = \pm \frac{b}{a}(x - h)$$ .

What is the definition of a parabola?

A parabola is a set of all points equidistant from a fixed point (focus) and a fixed line (directrix).

What is the significance of the parameter 'p' in the parabola's equation?

The parameter 'p' represents the distance from the vertex to the focus and the vertex to the directrix.

Hyperbola and Parabola TOTD Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

The center is (-1, 1).

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

The center is (0, 0).

4.

FLASHCARD QUESTION

Front

Back

The center is (-3, 2).

5.

FLASHCARD QUESTION

Front

What is the standard form of a parabola that opens to the right?

Back

6.

FLASHCARD QUESTION

Front

Back

The vertex is (0, 0).

7.

FLASHCARD QUESTION

Front

Back

The focus is located at (h+p, k) for a right-opening parabola.

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