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Splicer · Answer 1 · 2023-07-29T03:46:29+0000

Step-by-step explanation:

The equation of a circle is in the following form:

$\begin{gathered} (x\text{ - h\rparen}^2\text{ +\lparen y-k\rparen}^2\text{ = r}^2 \\ The\text{ center is found at \lparen h,k\rparen and the radius is r} \end{gathered}$

$\begin{gathered} We\text{ are given the following equation:} \\ x^2\text{ + y}^2\text{ + 8x -6y - 15 = 0} \\ To\text{ turn this equation into standard form, we need to complete the square for the x components and for the y components.} \\ ((x^2+8x\text{ +16\rparen -16\rparen+ \lparen\lparen y}^2-6y\text{ +9\rparen -9\rparen - 15 = 0} \\ (x+4)^2\text{ + \lparen y-3\rparen}^2\text{ = 15 + 9 +16} \\ (x+4)^2\text{ + \lparen y-3\rparen}^2\text{ = 40} \end{gathered}$

h = -4 and k = 3. r^2 = 40

Answer:

Center of the circle: (-4,3)

Radius:

$\begin{gathered} r\text{ = }\sqrt[]{40} \\ r\text{ = 2}√(10) \end{gathered}$

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