{"id":45063,"date":"2025-06-30T20:37:16","date_gmt":"2025-06-30T20:37:16","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=45063"},"modified":"2025-06-30T20:37:17","modified_gmt":"2025-06-30T20:37:17","slug":"write-an-equation-for-the-ellipse-graphed-in-standard-form","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-an-equation-for-the-ellipse-graphed-in-standard-form\/","title":{"rendered":"Write an equation for the ellipse graphed in standard form"},"content":{"rendered":"\n

Write an equation for the ellipse graphed in standard form:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

<\/p>\n\n\n\n

9 = 1<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To write the equation for the ellipse in standard form, we first need to identify its key features from the graph: the center, the orientation (horizontal or vertical), and the lengths of its major and minor axes.<\/p>\n\n\n\n

    \n
  1. Find the Center (h, k):<\/strong>
    The center of the ellipse is the midpoint of its longest diameter, the major axis. By observing the graph, we can see the ellipse’s rightmost point is at (3, -1) and its leftmost point is at (-7, -1). The center is halfway between these two points. We can find the x-coordinate of the center by averaging the x-coordinates of the vertices: h = (3 + (-7)) \/ 2 = -4 \/ 2 = -2. The y-coordinate remains -1. Therefore, the center of the ellipse, (h, k), is at (-2, -1).<\/li>\n\n\n\n
  2. Determine the Orientation and Semi-Major Axis (a):<\/strong>
    Since the ellipse is wider than it is tall, its major axis is horizontal. The standard form for a horizontal ellipse is (x – h)\u00b2\/a\u00b2 + (y – k)\u00b2\/b\u00b2 = 1. The value ‘a’ represents the length of the semi-major axis, which is the distance from the center to a vertex along the major axis. The distance from the center (-2, -1) to the right vertex (3, -1) is 5 units (3 – (-2) = 5). So, a = 5, and a\u00b2 = 25.<\/li>\n\n\n\n
  3. Determine the Semi-Minor Axis (b):<\/strong>
    The value ‘b’ represents the length of the semi-minor axis, which is the distance from the center to a co-vertex along the shorter minor axis. The top point of the ellipse is at (-2, 2) and the bottom point is at (-2, -4). The distance from the center (-2, -1) to the top co-vertex (-2, 2) is 3 units (2 – (-1) = 3). Thus, b = 3, and b\u00b2 = 9.<\/li>\n\n\n\n
  4. Write the Equation:<\/strong>
    Now we substitute the values for h, k, a\u00b2, and b\u00b2 into the standard equation for a horizontal ellipse:
    (x – h)\u00b2\/a\u00b2 + (y – k)\u00b2\/b\u00b2 = 1
    (x – (-2))\u00b2 \/ 25 + (y – (-1))\u00b2 \/ 9 = 1
    (<\/li>\n<\/ol>\n\n\n\n

    mos(experimental)<\/p>\n\n\n\n

    Auto<\/p>\n\n\n\n

    Expand to view model thoughtschevron_right<\/p>\n\n\n\n

    21.1seditmore_vert<\/p>\n\n\n\n

    x + 2)\u00b2 \/ 25 + (y + 1)\u00b2 \/ 9 = 1<\/p>\n\n\n\n

    This final equation accurately represents the ellipse shown on the graph.thumb_upthumb_down<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Write an equation for the ellipse graphed in standard form: The Correct Answer and Explanation is: 9 = 1 Explanation: To write the equation for the ellipse in standard form, we first need to identify its key features from the graph: the center, the orientation (horizontal or vertical), and the lengths of its major and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-45063","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=45063"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45063\/revisions"}],"predecessor-version":[{"id":45068,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45063\/revisions\/45068"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}