Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
The equation of the ellipse having foci (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].
Given the foci of ellipse is (±2,0) and vertices (±5,0).
We are required to find the equation of ellipse having foci (±2,0) and vertices (±5,0).
Equation is the relationship between two or more variables that are expressed in equal to form. Equation of two variables looks like ax+by=c.
Equation of ellipse is as under:
[tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex],where a is the semi major axis.
We have been given that a=5, c=2.
We know that [tex]c^{2} =a^{2} -b^{2}[/tex]
We have to find the value of b.
b=[tex]\sqrt{a^{2} -c^{2} }[/tex]
=[tex]\sqrt{5^{2} -2^{2} }[/tex]
=[tex]\sqrt{25-4}[/tex]
=[tex]\sqrt{21}[/tex]
Using the values of a and b in the equation [tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex]
[tex]x^{2} /(2)^{2} +y^{2}/\sqrt{21} ^{2} =1[/tex]
[tex]x^{2} /4+y^{2} /21=1[/tex]
Hence the equation of the ellipse having foci (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].
Learn more about ellipse at https://brainly.com/question/16904744
#SPJ4
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.