Answered

Find trusted answers to your questions with the help of IDNLearn.com's knowledgeable community. Ask anything and receive well-informed answers from our community of experienced professionals.

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

Write An Equation In Standard Form Of An Ellipse That Has A Vertex At 0 6 A Covertex At 1 0 And A Center At The Origin class=
Write An Equation In Standard Form Of An Ellipse That Has A Vertex At 0 6 A Covertex At 1 0 And A Center At The Origin class=
Write An Equation In Standard Form Of An Ellipse That Has A Vertex At 0 6 A Covertex At 1 0 And A Center At The Origin class=
Write An Equation In Standard Form Of An Ellipse That Has A Vertex At 0 6 A Covertex At 1 0 And A Center At The Origin class=

Sagot :

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

Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.