# What is the standard form of the equation of a circle with a center (-3, -4) and a radius of 3?

Mar 2, 2018

$\text{The equation of the circle with center" \ \ ( -3, -4 ) \qquad "and" \qquad "radius" \ \ 3, "in standard form, is:}$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad {\left(x + 3\right)}^{2} + {\left(y + 4\right)}^{2} \setminus = \setminus 9.$

#### Explanation:

$\text{Recall that the formula for the equation of a circle in standard}$ $\text{form is:}$

 \qquad \qquad \qquad \qquad \qquad \qquad \qquad ( x - h )^2 + ( y - k ) ^2 \ = \ r^2; \qquad \qquad \qquad \qquad \qquad \qquad \qquad (I)

$\setminus q \quad \setminus q \quad \text{where:" \qquad \qquad "center} \setminus = \setminus \left(h , k\right) ,$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus \quad \setminus \setminus \text{radius} \setminus = \setminus r .$

$\text{For the circle we are given, we have:}$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \text{center} \setminus = \setminus \left(\setminus {\overbrace{- 3}}^{h} , \setminus {\overbrace{- 4}}^{k}\right) ,$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus \quad \setminus \setminus \text{radius} \setminus = \setminus \setminus {\overbrace{3}}^{r} .$

$\text{So, substituting these values into (I), we get:}$

 \qquad \qquad \qquad \qquad \qquad \qquad \qquad ( x - h )^2 + ( y - k ) ^2 \ = \ r^2;

 \qquad \qquad \qquad \qquad \qquad ( x - ( -3 ) )^2 + ( y - ( -4 ) ) ^2 \ = \ 3^2;

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad {\left(x + 3\right)}^{2} + {\left(y + 4\right)}^{2} \setminus = \setminus 9.$

$\text{This is the equation of our given circle, in standard form.}$

$\text{Summarizing:}$

$\text{The equation of the circle with center" \ \ ( -3, -4 ) \qquad "and" \qquad "radius" \ \ 3, "in standard form, is:}$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad {\left(x + 3\right)}^{2} + {\left(y + 4\right)}^{2} \setminus = \setminus 9.$