Given the information below, write the equation in Standard Form.

Ellipse:

Vertices (-3, 7), (-3, 1)
Co-Vertices (-5, 4), (-1, 4)

The standard form of the equation  of the ellipse is  

Step-by-step explanation:

The standard form of the equation of an ellipse with center (h , k)  is

, where  

∵ The vertices of the ellipse are (-3 , 7), (-3 , 1)

∴ h = -3

∴ k + a = 7 ⇒ (1)

∴ k - a = 1 ⇒ (2)

- Add (1) and (2) to find k

∴ 2k = 8

- Divide both sides by 2

∴ k = 4

- Substitute the value of k in (1) or (2) to find a

∵ 4 + a = 7

- Subtract 4 from both sides

∴ a = 3

∵ The co-vertices of the ellipse are (-5 , 4), (-1 , 4)

∴ k = 4

∴ h - b = -5 ⇒ (1)

∴ h + b = -1 ⇒ (2)

∵ h = -3

- Substitute the value of h in (1) or (2) to find b

∴ -3 + b = -1

- Add 3 to both sides

∴ b = 2

∵ The standard form of the equation  of the ellipse is  

- Substitute the values of h, k, a, and b in the equation

∴  

∴  

The standard form of the equation  of the ellipse is  

x/3-10=8

x/3=18

x=48

the answer is the third / last answer

step-by-step explanation: