Find the Vertex Form 1/2x^2+1/8y^2=1/4

Problem

1/2*x2+1/8*y2=1/4

Solution

1. Identify the type of conic section. Since both x2 and y2 terms have positive coefficients, this is an ellipse. The "vertex form" for an ellipse centered at the origin is the standard form (x2)/(a2)+(y2)/(b2)=1

2. Multiply the entire equation by 4 to clear the fraction on the right side and set the constant term to 1

4⋅(1/2*x2+1/8*y2)=4⋅1/4

3. Distribute the 4 to each term on the left side of the equation.

2*x2+1/2*y2=1

4. Rewrite the coefficients as denominators to match the standard form (x2)/(a2)+(y2)/(b2)=1 Note that 2*x2 is equivalent to (x2)/(1/2) and 1/2*y2 is equivalent to (y2)/2

(x2)/(1/2)+(y2)/2=1

Final Answer

1/2*x2+1/8*y2=1/4⇒(x2)/(1/2)+(y2)/2=1

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