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

Problem

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

Solution

1. Identify the type of conic section. The equation is in the standard form of a vertical ellipse centered at the origin (0,0) because the denominator under y^2 is larger than the denominator under x^2

2. Determine the values of a^2 and b^2 In a vertical ellipse, the standard form is ((x−h)^2)/(b^2)+((y−k)^2)/(a^2)=1 where a>b

3. Extract the parameters. We have h=0 k=0 a^2=25 and b^2=9

4. Calculate the semi-major axis a and semi-minor axis b Taking the square roots gives a=5 and b=3

5. Locate the vertices. For a vertical ellipse, the vertices are located at (h,k±a) Substituting the values gives (0,0±5)

6. Locate the co-vertices. The co-vertices are located at (h±b,k) Substituting the values gives (0±3,0)

Final Answer

Vertices: *(0,5),(0,−5); Co-vertices: *(3,0),(−3,0)

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