Question

Can you show me how to write an equation of an ellipse centered at the origin, satisfying the given conditions? @mathmale

Answer 1

Conditions:

Vertex - \[(0, \sqrt{29} )\]

Co vertex - (-5, 0)

Answer 2

@mathmale @texaschic101 Help?

Answer 3

Hello, Nicole!

The equation of an ellipse centered at the origin is \[\frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2 }=1\]

Answer 4

If one vertex is \[(0, \sqrt{29} )\] and a co-vertex is (-5,0), then " a " represents the greater distance of these two points from the origin. That greater distance is \[ \sqrt{29}\] and " b " represents the distance of the co-vertex (horizontally) from the origin, or 5.

In summary, a=Sqrt(29) and b =5.

a^2 = 29 and b^2 =25

stick these 2 values into the general equation of an ellipse centered at the origin that I gave you, above.

Is this ellipse horiz. or vert.?

Answer 5

If vertical, then a^2 = 29 must go under y^2 in the equation; if horizontal, then a^2 = 29 must go under x^2 in the equation.

Answer 6

Oh my goodness! Thank you so much! I get everything but I'm unsure on the determination of the ellipse being horiz or vert.. I forget which is which.

Answer 7

Which is greater, 5 or Sqrt(29)? That will tell you whether your ellipse is vert. or horiz. :)

Answer 8

Sqrt(29) is bigger. @mathmale

Answer 9

Right. Is that on the y-axis or on the x-axis? 25 goes under one of the following: x^2 or y^2; Sqrt(29) goes under the other one. Which?

Answer 10

25 under x and sqrt(29) under y ??

Answer 11

Exactly. Nice work, Nicole!!

Answer 12

Thank you again (: