Final answer:
To find the center (h,k) and radius r of the circle represented by the equation x²y² - 4x - 2y = 0, rewrite the equation in standard form and identify the center and radius. Then, graph the circle and find the intercepts by substituting 0 for x and y.
Step-by-step explanation:
To find the center (h,k) and radius r of the circle represented by the equation x²y² - 4x - 2y = 0:
(a) First we need to rewrite the equation in the standard form of a circle, which is (x - h)² + (y - k)² = r². To do this, we complete the square for both the x and y terms.
(b) Once we have the equation in standard form, we can identify the center (h,k) and radius r.
(c) To graph the circle, we plot the center and draw a circle with the given radius.
(d) To find the intercepts, we substitute 0 for x and y in the equation and solve for the remaining variable.