Find the center (h,k) and radius r of the circle. Graph the equation. x^2 + y^2 - 2x - 10y + 1 = 0

2 answers
Question:

Find the center (h,k) and radius r of the circle. Graph the equation. x^2 + y^2 - 2x - 10y + 1 = 0

Answers

Answer:Center: (1, 5)Radius: r = 5Step-by-step explanation:Step 1: Rewrite equationx² - 2x + y² - 10y = -1Step 2: Complete the Square (x2)x² - 2x + 1 + y² -10y + 25 = -1 + 1 + 25(x - 1)² + (y - 5)² = 25Step 3: Find answersCenter = (h, k)(1, 5) as CenterRadius = rr² = 25r = 5

Answer: Center = (1, 5)                Radius = 5Step-by-step explanation:The standard form for a circle is: (x - h)² + (y - k)² = r²     whereCenter = (h, k)Radius = rFirst, group the x's and group the y's in order to complete the square.x² - 2x        + y² - 10y         = -1      ↓                    ↓    (-2/2)²=1         (-10/2)²=25Add those values to BOTH sides:x² - 2x + 1      +  y² - 10y + 25    = -1 + 1 + 25Rewrite the left side as perfect squares and simplify the right side.   (x - 1)²       +     (y - 5)²         = 25We end up with (h, k) = (1, 5)   this is the center         and r² = 25 --> r = 5         this is the radiusTo graph the circle, place an x at the center (1, 5).  Plot a point 5 units (the radius) to the right of the center, another point 5 units up from the center, a third point 5 units left from the center, and a fourth point 5 units down from the center. "Connect the dots" to create a circle.

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