Problem 47450. Area of Ellipse

Created by Soobok

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Caculate the area of below ellipse.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>$$\\frac{x^{2}}{a^2}+\\frac{y^{2}}{b^2}=1$$</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>So, input x = [a b], numeric vector when a, b are not zero.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 95.6667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 47.8333px; transform-origin: 406.5px 47.8333px; vertical-align: baseline; "><div style="block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Caculate the area of below ellipse.</span></span></div><div style="block-size: 36.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 18.1667px; text-align: left; transform-origin: 383.5px 18.1667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-16px"><img src="data:image/png;base64,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" width="71.5" height="36.5" style="width: 71.5px; height: 36.5px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">.</span></span></div><div style="block-size: 20.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.3333px; text-align: left; transform-origin: 383.5px 10.3333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">So, input x = [a b], numeric vector when a, b are not zero.</span></span></div></div></div>

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Last Solution submitted on Jun 16, 2022

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2 Comments

Dyuman Joshi on 23 Nov 2020

I think the problem answer is incorrect.
The area is pi*a*b for a standard ellipse (x^2/a^2 + y^2/b^2 = 1)
and not the one that is mentioned. So according to the problem statement, the answer should be pi*sqrt(a*b)

Soobok on 23 Nov 2020

Thank you Dyuman.
I missed the terms of the square.
I modified the form of the ellipse equation.

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Problem 47450. Area of Ellipse

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Problem 47450. Area of Ellipse

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