Find the center, vertices, and foci of the ellipse with equation 5x2 + 8y2 = 40.

Center of the ellipse = (0, 0)

vertices are (±√8, 0) and (0, ±√5)

Focus of the ellipse =  (±√3, 0).

Step-by-step explanation:

Equation of an ellipse is given as 5x² + 8y² = 40

We will rewrite this equation in the vertex form

⇒

⇒

This equation is in the form of

⇒

Then Center of the ellipse is (h, k) and major vertices will be (h±a, k) with minor vertices will be (h, k±b)

and focus is (h±c, k) where c =

Now we put the values h = 0 and k = 0

Center of this ellipse will be (0, 0)

Vertices of the ellipse will be

Major vertices = (0±√8, 0) = (±√8, 0)

Minor vertices = (0, 0±√5) = (0, ±√5)

Now Focus of the ellipse = (0±c, 0)

where c = √(a² - b²) = √(8-5) = √3

Now focus is (±√3, 0).

1.30

step-by-step explanation: