Question

chapter 7:7.1-7.2
due: tue jun 23, 2026 11:59pm

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chapter 7:7.1-7.2
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question 1

find the center and radius of the circle whose equation is (x^2 - 5x + y^2 - 4y - 12 = 0).

the center of the circle is (\\_, \\_).
the radius of the circle is \\_.

question help: video

Explanation:

Step1: Group terms and move constant

$$(x^2 - 5x) + (y^2 - 4y) = 12$$

Step2: Complete the square

$$(x^2 - 5x + \frac{25}{4}) + (y^2 - 4y + 4) = 12 + \frac{25}{4} + 4$$

Step3: Simplify the equation

$$(x - \frac{5}{2})^2 + (y - 2)^2 = \frac{81}{4}$$

Step4: Identify center and radius

$$\text{Center} = (\frac{5}{2}, 2), \quad \text{Radius} = \sqrt{\frac{81}{4}} = \frac{9}{2}$$

Answer:

The center of the circle is \((\frac{5}{2}, 2)\).
The radius of the circle is \(\frac{9}{2}\).