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Write the equation in standard form. Then identify the center and diameter.
15.
x^(2)+y^(2)+14 x+10 y+73=0

Write the equation in standard form. Then identify the center and diameter. $\newline$ $15$ . $x^{2}+y^{2}+14 x+10 y+73=0$

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Find derivatives of using multiple formulae

Full solution

Q. Write the equation in standard form. Then identify the center and diameter.

\newline

15

.

x^{2}+y^{2}+14 x+10 y+73=0

Rewrite Equation: Rewrite the given equation in standard form for a circle by completing the square for both $x$ and $y$ terms. $\newline$ $x^2 + 14x + y^2 + 10y + 73 = 0$ $\newline$ For $x$ : $x^2 + 14x \rightarrow (x + 7)^2 - 49$ $\newline$ For $y$ : $y^2 + 10y \rightarrow (y + 5)^2 - 25$ $\newline$ Substitute back into the equation: $\newline$ $(x + 7)^2 - 49 + (y + 5)^2 - 25 + 73 = 0$ $\newline$ $(x + 7)^2 + (y + 5)^2 - 1 = 0$
Simplify Equation: Simplify the equation to get the standard form of the circle. $\newline$ $(x + 7)^2 + (y + 5)^2 = 1$
Identify Center and Diameter: Identify the center and diameter of the circle. $\newline$ Center: $(-7, -5)$ $\newline$ Radius: $\sqrt{1} = 1$ $\newline$ Diameter = $2 \times$ Radius = $2 \times 1 = 2$

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