Write an equation in standard form of an ellipse that has a vertex at (0,6), and a co-vertex at (1,0), and an center at the origin

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

ANSWER

EXPLANATION

The equation of an ellipse in standard form with vertices on the y-axis and center at the origin is given by:

where

a=6 and b=1

We plug in these value into the formula to get:

its 60

4 x 12 = 48

3 x 4 = 12

48 + 12 = 60

yeeeet