Question

the equation of a circle is given in standard form. complete parts a through c to follow the step by step process to sketch the graph of the circle. (x - 1)^2+(y + 8)^2 = 4 c) determine the x - and y - intercepts of the circle. select the correct choice and, if necessary, fill in the answer box within your choice. a. the x - intercept(s) is/are x =. (use a comma to separate answers as needed. type an exact answer, using radicals as needed.) b. there is no x - intercept. select the correct choice and, if necessary, fill in the answer box within your choice. a. the y - intercept(s) is/are y =. (use a comma to separate answers as needed. type an exact answer, using radicals as needed.) b. there is no y - intercept.

Explanation:

Step1: Find x - intercepts

Set \(y = 0\) in the equation \((x - 1)^2+(y + 8)^2=4\). We get \((x - 1)^2+(0 + 8)^2=4\), which simplifies to \((x - 1)^2+64 = 4\), then \((x - 1)^2=4 - 64=-60\). Since the square of a real - number cannot be negative, there are no real x - intercepts.

Step2: Find y - intercepts

Set \(x = 0\) in the equation \((x - 1)^2+(y + 8)^2=4\). We have \((0 - 1)^2+(y + 8)^2=4\), so \(1+(y + 8)^2=4\), then \((y + 8)^2=3\). Taking the square root of both sides, \(y+8=\pm\sqrt{3}\), and \(y=-8\pm\sqrt{3}\).

Answer:

B. There is no x - intercept.
A. The y - intercept(s) is/are \(y=-8+\sqrt{3},-8 - \sqrt{3}\)