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

Equation of the Ellipse is

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,

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

Therefore, Equation of the Ellipse is

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x