Find the Properties (x^2)/9+(y^2)/25=1

Problem

(x2)/9+(y2)/25=1

Solution

1. Identify the type of conic section. Since the equation is in the form (x2)/(b2)+(y2)/(a2)=1 with a>b it is a vertical ellipse centered at the origin (0,0)

2. Determine the values of a and b We have a2=25 so a=5 We have b2=9 so b=3

3. Calculate the distance to the foci c using the relationship c2=a2−b2

c2=25−9

c2=16

c=4

4. Identify the vertices and co-vertices. The vertices are located at (0,±a) and the co-vertices are at (±b,0)

Vertices⇒(0,5),(0,−5)

Co-vertices⇒(3,0),(−3,0)

5. Identify the foci. The foci are located on the major axis at (0,±c)

Foci⇒(0,4),(0,−4)

6. Calculate the eccentricity e using the formula e=c/a

e=4/5

Final Answer

Center: *(0,0), Vertices: *(0,±5), Foci: *(0,±4), Eccentricity: 4/5

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