Answer: [tex]\dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
Step-by-step explanation:
General equation of ellipse : [tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}[/tex]
Given: Vertices of ellipse : (± 9,0)
Since the vertices are of the form (± a, 0).
i.e. a=9
Thus, the major axis is along x-axis.
Also, foci of the ellipse = (±5,0)
Since, foci is of the form (± c,0), i.e. c=5
Since
[tex]c^2=a^2-b^2\\\\\Rightarrow\ 5^2= 9^2-b^2\\\\\Rightarrow\ b^2=81-25\\\\\Rightarrow\ b^2=56[/tex]
Equation of ellipse :
[tex]\dfrac{x^2}{9^2}+\dfrac{y^2}{56}=1\\\\\Rightarrow\ \dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
Hence, the required equation : [tex]\dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
