Question

ard equation for each of the circles in parts (a) through (c). the coordinates
nd the radius for each circle are integers.

uation of the circle in standard form is ( x^2 + y^2 = 25 ).
equation. simplify your answer.)

thats incorrect.
correct answer: ( (x - 3)^2 + y^2 = 20 )
your answer: ( (x - 3)^2 + y^2 = 26 )
) the equation of the circ
type an equation. simplify

Explanation:

To determine the standard equation of a circle, we use the formula \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step 1: Identify the center

Assuming the center of the circle is \((3, 0)\) (from the correct answer's form \((x - 3)^2 + y^2 = 20\)), so \(h = 3\) and \(k = 0\).

Step 2: Calculate the radius squared

The correct equation is \((x - 3)^2 + y^2 = 20\), which means \(r^2 = 20\). Let's verify how we get this. If we made a mistake earlier (like in the incorrect answer \((x - 3)^2 + y^2 = 26\)), we must have miscalculated the radius. Suppose we have a point on the circle or some other information (not fully visible here, but the correct answer is given as \((x - 3)^2 + y^2 = 20\)). So using the standard form, with center \((3, 0)\) and \(r^2 = 20\), the equation is \((x - 3)^2 + y^2 = 20\).

Answer:

\((x - 3)^2 + y^2 = 20\)