Question

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5

Answer 1

Equation of the Ellipse is
`(x^2)/(21)+(y^2)/(25)=1`

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,

`(x^2)/(b^2)+(y^2)/(a^2)=1`

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

`(x^2)/((√(21))^2)+(y^2)/(5^2)=1`

`(x^2)/(21)+(y^2)/(25)=1`

Therefore, Equation of the Ellipse is
`(x^2)/(21)+(y^2)/(25)=1`

Answer 2

The equation is asking to calculate the standard for of the equation of ellipse satisfying the given condition and in my further research and computation, would say that the answer would be x^2/21 + y^2/25 = 1. I hope you are satisfied with my answer and feel free to ask for more