Question

multiple choice 10 points a circle has the equation ((x - 3)^2 + (y + 5)^2 = 36). which of the following statements is not true? the point (3, 1) lies on the circle. the y - coordinate of the center is 5. the radius of the circle is 6. the x - coordinate of the center is 3. clear my selection previous

Explanation:

Step1: Recall the standard circle equation

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. For the given equation \((x - 3)^2 + (y + 5)^2 = 36\), we can identify \(h = 3\), \(k=- 5\), and \(r^2=36\) so \(r = 6\).

Step2: Analyze each option

• Option 1: Check if \((3,1)\) lies on the circle. Substitute \(x = 3\), \(y = 1\) into the left - hand side of the equation: \((3 - 3)^2+(1 + 5)^2=0 + 36=36\), which is equal to the right - hand side. So the point \((3,1)\) lies on the circle.
• Option 2: The y - coordinate of the center \(k=-5\), not 5.
• Option 3: The radius \(r=\sqrt{36}=6\), so this statement is true.
• Option 4: The x - coordinate of the center \(h = 3\), so this statement is true.

Answer:

The y - coordinate of the center is 5.