Final answer:
Complete the square to find the center (h, k) and radius r of the given circle's equation. Plot the center (1, 3) on the coordinate plane and draw a circle with a radius of 6. Calculate intercepts by setting x and y to 0 in the original equation.
Step-by-step explanation:
To find the center (h,k) and radius r of the circle given by the equation x² + y² - 2x - 6y − 26 = 0, we need to complete the square for both x and y.
The equation can be rewritten in the form: (x - h)² + (y - k)² = r² by completing the squares as follows:
- Group the x terms together and the y terms together.
- Add and subtract the square of half the coefficient of x, which is 1 (since (1/2)(2) = 1 and 1² = 1).
- Add and subtract the square of half the coefficient of y, which is 9 (since (1/2)(6) = 3 and 3² = 9).
- Rewrite the equation: (x² - 2x + 1) + (y² - 6y + 9) = 26 + 1 + 9.
- Simplify to get the equation in standard circle form: (x - 1)² + (y - 3)² = 36.
From this form, we can see the center of the circle is (1, 3) and the radius is 6.
Graphing the circle would involve drawing a circle with a center at (1, 3) and a radius of 6 on a standard coordinate plane.
To find the x and y intercepts, we set y and x to 0 in the equation and solve for the other variable respectively.