How to Find the Parabola Equation with a Focus of 60 and Vertex (0, 0)

Determining the equation of a parabola with a specific focus and vertex is a common problem in mathematics. This article will guide you through the process, providing a detailed explanation and emphasizing the SEO optimization of your content. By focusing on keywords, structural HTML, and readability, we can ensure that this article is not only informative but also easily discoverable on search engines like Google.

Understanding the Parabola

A parabola is a curve where any point is at an equal distance from a fixed point (focus) and a fixed straight line (directrix). The equation of a parabola with a vertical axis of symmetry and vertex at the origin is typically written as y^2 4ax.

Given Conditions:

Focus: (6, 0) Vertex: (0, 0)

Our goal is to determine the equation of the parabola with these given parameters.

Step-by-Step Solution

Using the definitions of the parabola, we know that for any point (x, y) on the parabola, the distance from this point to the focus is equal to the distance from this point to the directrix.

The distance from (x, y) to the focus (6, 0) is given by:

sqrt{(x - 6)^2 (y - 0)^2}

The distance from (x, y) to the directrix (x -6) is given by:

|x - (-6)| |x 6|

Equating these distances, we get:

sqrt{(x - 6)^2 y^2} |x 6|

Squaring both sides to eliminate the square root, we have:

(x - 6)^2 y^2 x^2 12x 36

Expanding and simplifying:

x^2 - 12x 36 y^2 x^2 12x 36

y^2 - 12x 12x

y^2 24x

x y^2 / 24

SEO Optimization

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We have also structured the content with proper headings and paragraphs to enhance readability and make it easier for search engines to understand the context. Additionally, we have included relevant images and diagrams to visually represent the concepts discussed.

Conclusion

By following the steps outlined in this article, you can now find the equation of a parabola with a focus and vertex. Effective SEO practices ensure that your content is not only accurate but also easily discoverable by search engines, making it valuable for students, educators, and anyone seeking to understand parabolic properties.

Keywords for SEO: parabola equation, vertex and focus, directrix

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