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Find the vertex, focus, and directrix of the parabola. x² = 6y vertex focus directrix (x, y) (x, y) Sketch its graph. = 0.0 3 (0, 1/1 2 X

Find the vertex, focus, and directrix of the parabola. x² = 6y vertex focus directrix (x, y) (x, y) Sketch its graph. = 0.0 3 (0, 1/1 2 X

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Can u pls help me find the diretix
The image provides an example of how to find the vertex, focus, and directrix of a parabola with the equation \( x^2 = 6y \). **Vertex** - Coordinates: \( (x, y) = (0, 0) \) **Focus** - Coordinates: \( (x, y) = \left(0, \frac{3}{2}\right) \) **Directrix** - The directrix line is not correctly completed in the input field, marked with a red cross indicating an error. **Graph Explanation** - *Diagram on the left*: A parabola with its vertex at the origin \((0, 0)\) is shown. It opens upwards, indicating that its axis of symmetry is the y-axis. - The focus is marked at \( \left(0, \frac{3}{2}\right) \). - Two dashed red lines likely represent the directrix, which is parallel to the x-axis. The correct line is not specified, but it should be at \( y = -\frac{3}{2} \) to correspond to the given focus. This graph visually represents the characteristics of the parabola, helping in understanding how its focus and directrix influence its shape.
Transcribed Image Text:The image provides an example of how to find the vertex, focus, and directrix of a parabola with the equation \( x^2 = 6y \). **Vertex** - Coordinates: \( (x, y) = (0, 0) \) **Focus** - Coordinates: \( (x, y) = \left(0, \frac{3}{2}\right) \) **Directrix** - The directrix line is not correctly completed in the input field, marked with a red cross indicating an error. **Graph Explanation** - *Diagram on the left*: A parabola with its vertex at the origin \((0, 0)\) is shown. It opens upwards, indicating that its axis of symmetry is the y-axis. - The focus is marked at \( \left(0, \frac{3}{2}\right) \). - Two dashed red lines likely represent the directrix, which is parallel to the x-axis. The correct line is not specified, but it should be at \( y = -\frac{3}{2} \) to correspond to the given focus. This graph visually represents the characteristics of the parabola, helping in understanding how its focus and directrix influence its shape.
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