Find the Properties (x^2)/36+(y^2)/25=1

Problem

(x2)/36+(y2)/25=1

Solution

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

2. Determine the values of a and b We have a2=36 which gives a=6 and b2=25 which gives b=5

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

c2=36−25

c2=11

c=√(,11)

4. Find the vertices and co-vertices. The vertices are at (±a,0) which are (±6,0) The co-vertices are at (0,±b) which are (0,±5)

5. Locate the foci. The foci are at (±c,0) which are (±√(,11),0)

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

e=√(,11)/6

Final Answer

Center: *(0,0), Vertices: *(±6,0), Co-vertices: *(0,±5), Foci: *(±√(,11),0), Eccentricity: √(,11)/6

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