Answer:
The standard equation is x²/16 + y²/49 = 1
Explanation:
* Lets revise the standard equation of the ellipse
- The standard form of the equation of an ellipse with
center (0 , 0) is x²/b² + y²/a² = 1 , where
* The coordinates of the vertices are (0 , ± a)
* The coordinates of the foci are (0 , ± c), where c² = a² - b²
* Now lets solve the problem
∵ The vertices of the ellipse are (0 , -7) , (0 , 7)
∵ The coordinates of the vertices are (0 , - a) , (0 , a)
∴ a = 7 , -7
∵ The coordinates of the foci are (0 , -√33) , (0 , √33)
∵ The coordinates of the foci are (0 , - c) , (0 , c)
∴ c = -√33 , √33
∵ c² = a² - b²
∵ a² = (7)² = 49
∵ c² = (√33)² = 33
∴ 33 = 49 - b² ⇒ subtract 49 from both sides
∴ -16 = -b² ⇒ multiply both sides by -1
∴ b² = 16
∵ The standard equation of the ellipse is x²/b² + y²/a² = 1
∴ The standard equation is x²/16 + y²/49 = 1