Find the Vertex Form x^2+y^2=25

Problem

x2+y2=25

Solution

1. Identify the type of equation. This is the standard form of a circle centered at the origin (h,k)=(0,0) with radius r

2. Recall the standard vertex (center-radius) form for a circle, which is (x−h)2+(y−k)2=r2

3. Rewrite the terms x2 and y2 to explicitly show the coordinates of the center.

4. Substitute x2 with (x−0)2 and y2 with (y−0)2

5. Determine the radius by identifying r2=25 which means r=5

Final Answer

(x−0)2+(y−0)2=25

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