Answer:
Equation of the Ellipse is [tex]\frac{x^2}{21}+\frac{y^2}{25}=1[/tex]
Step-by-step explanation:
Given:
Foci ( 0 , -2 ) and ( 0 , 2 )
y-intercept = -5 and 5
To find: standard form of the Equation of the ellipse.
Since, x-coordinate of the foci are 0.
⇒ Major axis of the Ellipse is y-axis.
⇒ Standard Equation of the ellipse,
[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]
Now, from y-intercept a = 5 and from foci, c = 2
⇒ c² = a² - b²
2² = 5² - b²
b² = 25 - 4
b² = 21
b = ± √21
So, equation is
[tex]\frac{x^2}{(\sqrt{21})^2}+\frac{y^2}{5^2}=1[/tex]
[tex]\frac{x^2}{21}+\frac{y^2}{25}=1[/tex]
Therefore, Equation of the Ellipse is [tex]\frac{x^2}{21}+\frac{y^2}{25}=1[/tex]
