Skip to main content
Ch. 7 - Conic Sections
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 7 - Conic SectionsProblema 25
Capitolo 8, Problema 25

Find the standard form of the equation of each parabola satisfying the given conditions. Vertex: (2, - 3); Focus: (2, - 5)

Guida verificata passo dopo passo
1
Identify the vertex \( V = (2, -3) \) and the focus \( F = (2, -5) \). Since the x-coordinates are the same, the parabola opens vertically (either up or down).
Calculate the distance \( p \) between the vertex and the focus. This distance determines how far the parabola opens from the vertex. Use the formula \( p = y_{focus} - y_{vertex} \).
Write the standard form of the parabola that opens vertically: \( (x - h)^2 = 4p(y - k) \), where \( (h, k) \) is the vertex.
Substitute the vertex coordinates \( (h, k) = (2, -3) \) and the value of \( p \) found in step 2 into the equation.
Simplify the equation to get the standard form of the parabola.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Definition of a Parabola

A parabola is the set of all points equidistant from a fixed point called the focus and a fixed line called the directrix. Understanding this definition helps in deriving the equation of the parabola when the vertex and focus are known.
Video consigliato:
5:28
Horizontal Parabolas

Standard Form of a Parabola

The standard form of a parabola's equation depends on its orientation. For vertical parabolas, it is (x - h)^2 = 4p(y - k), and for horizontal parabolas, (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus.
Video consigliato:
5:33
Parabolas as Conic Sections

Finding the Parameter p

The parameter p represents the distance from the vertex to the focus (or directrix) and determines the parabola's width and direction. Calculating p from the given vertex and focus coordinates is essential to write the equation in standard form.
Video consigliato:
3:43
Finding the Domain of an Equation
Pratica correlata
Domanda del libro di testo

Find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (-5, 0), (5, 0); vertices: (-8, 0), (8,0)

1010
views
Domanda del libro di testo

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci: (-8,0), (8,0); Vertices: (-3,0), (3,0)

1420
views
Domanda del libro di testo

Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the equations of the asymptotes.y=±x2−2y = \(\pm\)\(\sqrt{x^2 - 2}\)

768
views
Domanda del libro di testo

Find the standard form of the equation of each ellipse and give the location of its foci.

848
views
Domanda del libro di testo

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci: (0,-4), (0,4); Vertices: (0, -2), (0,2)

1010
views
Domanda del libro di testo

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, - 25); Directrix: y = 25

741
views