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

HJStep-by-step explanation:it is what it is...

Find the center, vertices, and foci of the ellipse

jadacherry

31.12.2021

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

$\frac{5x^{2}+8y^{2}}{40}=\frac{40}{40}$

⇒ $\frac{x^{2}}{8}+\frac{y^{2}}{5}=1$

⇒ $\frac{(x-0)^{2}}{8}+\frac{(y-0)^{2}}{5}=1$

This equation is in the form of

⇒ $\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1$

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 = $\sqrt{a^{2}-b^{2}}$

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).

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