Question

What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)? HELP

A: x^2 + y^2 − 4x + 2y + 1 = 0

B: x^2 + y^2 + 4x − 2y + 1 = 0

C: x^2 + y^2 + 4x − 2y + 9 = 0

D: x^2 − y^2 + 2x + y + 1 = 0

Answer 1

\(\large\color{black}{ \displaystyle (x-h)^2+(y-k)^2=r^2 }\)
is the formula for the equation of the circle,

WHERE:
a) \(\large\color{black}{ \displaystyle (h,k) }\) is the center
b) \(\large\color{black}{ \displaystyle r }\) is the radius.

Answer 2

the center you are already given, and then you will need to use the distance formula
between your 2 points to find the radius.

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

DISTANCE FORMULA:

\(\Large\color{black}{ \displaystyle {\rm D} =\sqrt{ (\color{blue}{{\rm y}_1}-\color{red}{{\rm y}_2})^2+(\color{green}{{\rm x}_1}-\color{darkgoldenrod}{{\rm x}_2})^2 }}\)

where,
\(\Large\color{black}{ \displaystyle {\rm D} }\) is the distance.

\(\Large\color{black}{ \displaystyle (\color{green}{{\rm x}_1}~,~~\color{blue}{{\rm y}_1}) }\) and \(\Large\color{black}{ \displaystyle (\color{darkgoldenrod}{{\rm x}_2}~,~~\color{red}{{\rm y}_2}) }\) are your two points.

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)