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

Problem

1/2*x^2+1/8*y^2=1/4

Solution

1. Identify the type of conic section. Since both x^2 and y^2 terms have positive coefficients, this is an ellipse. The "vertex form" for an ellipse centered at the origin is the standard form (x^2)/(a^2)+(y^2)/(b^2)=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*x^2+1/8*y^2)=4⋅1/4

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

2*x^2+1/2*y^2=1

4. Rewrite the coefficients as denominators to match the standard form (x^2)/(a^2)+(y^2)/(b^2)=1 Note that 2*x^2 is equivalent to (x^2)/(1/2) and 1/2*y^2 is equivalent to (y^2)/2

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

Final Answer

1/2*x^2+1/8*y^2=1/4⇒(x^2)/(1/2)+(y^2)/2=1

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