Find the Vertex Form (x^2)/4+(y^2)/25=1

Problem

(x2)/4+(y2)/25=1

Solution

1. Identify the type of conic section. The equation is in the standard form of an ellipse centered at the origin (0,0) because it follows the form (x2)/(a2)+(y2)/(b2)=1

2. Determine the values of a2 and b2 From the equation, we see that the denominator under x2 is 4 and the denominator under y2 is 25

3. Calculate the semi-axes lengths. Since b2=25 is greater than a2=4 the ellipse is vertically oriented.

a=√(,4)=2

b=√(,25)=5

4. Locate the vertices. For a vertical ellipse centered at (h,k) the vertices are located at (h,k±b) Here, (h,k)=(0,0) and b=5

(V_1)=(0,5)

(V_2)=(0,−5)

5. Locate the co-vertices. The co-vertices are located at (h±a,k) Here, a=2

(C_1)=(2,0)

(C_2)=(−2,0)

6. Express in vertex form. For an ellipse, the "vertex form" is the standard form showing the center (h,k)

((x−h)2)/(a2)+((y−k)2)/(b2)=1

Final Answer

(x2)/4+(y2)/25=1⇒((x−0)2)/2+((y−0)2)/5=1

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