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

Problem

x^2+y^2=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=r^2

3. Rewrite the terms x^2 and y^2 to explicitly show the coordinates of the center.

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

5. Determine the radius by identifying r^2=25 which means r=5

Final Answer

(x−0)^2+(y−0)^2=25

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