Answer:
The standard form of the equation of the ellipse is x² + y²/36 = 1
Step-by-step 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 length of the major axis is 2a
* the coordinates of the vertices are (0 , ±a)
* the length of the minor axis is 2b
* the coordinates of the co-vertices are (±b , 0)
* the coordinates of the foci are (0 , ± c), where c² = a² - b²
* Now lets solve the problem
∵ The vertex of the ellipse is (0 , 6)
∴ a = 6
∵ The co-vertex is (1 , 0)
∴ b = 1
∵ the center is the origin (0 , 0)
∵ The standard form equation is x²/b² + y²/a² = 1
∴ x²/(1)² + y²/(6)² = 1 ⇒ simplify
∴ x² + y²/36 = 1
* The standard form of the equation of the ellipse is x² + y²/36 = 1
