Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
for an ellipse x²/a² + y²/a² = 1
vertices are -a,0 a, 0 0,b 0, -b focus : √(a²-b²) , 0
center is origin 0,0
given ellipse : divide by 40 on both sides
x² / 8 + y²/5 = 1
So a = √8 = 2√2 b = √5
vertices are -2√2,0 2√2,0 0,√5 0,-√5
focii = √3, 0 -√3, 0
vertices are -a,0 a, 0 0,b 0, -b focus : √(a²-b²) , 0
center is origin 0,0
given ellipse : divide by 40 on both sides
x² / 8 + y²/5 = 1
So a = √8 = 2√2 b = √5
vertices are -2√2,0 2√2,0 0,√5 0,-√5
focii = √3, 0 -√3, 0
Answer:
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
[tex]\frac{5x^{2}+8y^{2}}{40}=\frac{40}{40}[/tex]
⇒[tex]\frac{x^{2}}{8}+\frac{y^{2}}{5}=1[/tex]
⇒[tex]\frac{(x-0)^{2}}{8}+\frac{(y-0)^{2}}{5}=1[/tex]
This equation is in the form of
⇒[tex]\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1[/tex]
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 =[tex]\sqrt{a^{2}-b^{2}}[/tex]
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).
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.