What is the equation that represents the circle shown on the coordinate plane, in standard Pythagorean Theorem form?

Question

(1 point)
Responses

(x−1)2+(y−2)2=5 open paren x minus 1 close paren squared plus open paren y minus 2 close paren squared is equal to 5

(x+1)2+(y−2)2=5 open paren x plus 1 close paren squared plus open paren y minus 2 close paren squared is equal to 5

(x+2)2+(y−1)2=25 open paren x plus 2 close paren squared plus open paren y minus 1 close paren squared is equal to 25

(x−2)2+(y−1)2=25

Answer 1

The equation of a circle in standard form is given by:

\[ (x - h)^2 + (y - k)^2 = r^2 \]

where \((h, k)\) is the center of the circle, and \(r\) is the radius.

The options provided seem to suggest different centers and radii. To determine the correct equation, you need to identify the center and radius from the circle depicted on the coordinate plane.

• \((x - 1)^2 + (y - 2)^2 = 5\) indicates a center at \((1, 2)\) with a radius of \(\sqrt{5}\).
• \((x + 1)^2 + (y - 2)^2 = 5\) indicates a center at \((-1, 2)\) with a radius of \(\sqrt{5}\).
• \((x + 2)^2 + (y - 1)^2 = 25\) indicates a center at \((-2, 1)\) with a radius of \(5\).
• \((x - 2)^2 + (y - 1)^2 = 25\) indicates a center at \((2, 1)\) with a radius of \(5\).

Choose the correct option based on the center and radius of the circle shown on the coordinate plane. If you cannot visually identify the circle, you may need to provide further context or data regarding the circle in question to determine the correct answer.