Question

(a) find the following. radius: 2 units center: (3, 7) value of a: select ^ value of b: x - 4 4 - x (b) use the pythago relating the side your answer in t letters). 4 - y y - 7 (x - 3)^2 + y - 4 = (2)^2 7 - x x - 7 7 - y em to write an equati the right triangle. wri ind y (with no other)

Explanation:

Step1: Recall the standard form of a circle equation

The standard - form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius. Given the center \((h,k)=(3,7)\) and radius \(r = 2\).

Step2: Identify the values for the equation

For the equation \((x - a)^2+(y - b)^2=r^2\), comparing with the standard - form, we have \(a = 3\) and \(b = 7\).

Step3: Use the Pythagorean theorem for part (b)

The distance between a point \((x,y)\) on the circle and the center \((3,7)\) is equal to the radius. By the Pythagorean theorem, if the horizontal distance between the point \((x,y)\) and the center \((3,7)\) is \(x - 3\) and the vertical distance is \(y - 7\), the equation of the circle is \((x - 3)^2+(y - 7)^2=4\).

Answer:

(a) Value of \(a\): \(3\), Value of \(b\): \(7\)
(b) \((x - 3)^2+(y - 7)^2=4\)