Question

What is the standard form of the equation of a circle with its center at (2, -3) and passing through the point (-2, 0)?

Answer 1

1st find the distance of centre using distance formula...

then use this

(x-x1)^2+(y-y1)^2=c^2

c=centre
x1=-2
y1=0

Answer 2

(x − 2)2 + (y + 3)2 = 5

(x + 2)2 + (y − 3)2 = 25

(x − 2)2 + (y + 3)2 = 25

(x − 2)2 − (y + 3)2 = 5

Answer 3

those are the answer options

Answer 4

use the distnace formula to find the radius firstly, thus \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
center&({\color{red}{ 2}}\quad ,&{\color{blue}{ -3}})\quad point&({\color{red}{ -2}}\quad ,&{\color{blue}{ 0}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)


keep in mind that \(\bf (x-{\color{brown}{ h}})^2+(y-{\color{blue}{ k}})^2={\color{olive}{ r}}^2\qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad radius={\color{olive}{ r}}\)

Answer 5

hmmm so \(\b \bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
center&({\color{red}{ 2}}\quad ,&{\color{blue}{ -3}})\quad point&({\color{red}{ -2}}\quad ,&{\color{blue}{ 0}})
\end{array}
\\ \quad \\

d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 6

I'm so confused.
would it be a=5
B=25
C=25
or D=5

Answer 7

?

Answer 8

A (x − 2)2 + (y + 3)2 = 5

B (x + 2)2 + (y − 3)2 = 25

C (x − 2)2 + (y + 3)2 = 25

D (x − 2)2 − (y + 3)2 = 5

Answer 9

so... what did you get for the radius?

Answer 10

What is the standard form of the equation of a circle with its center at (2, -3) and passing through the point (-2, 0)

Answer 11

we read that, yes

Answer 12

thats the question it isn't asking for a radius, it wants the standard equation.. thats why I said A B C or D

Answer 13

it was C i guessed :)

Answer 14

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?

Answer 15

(-7, -1), 36 units

(7, 1), 36 units

(7, 1), 6 units

(-7, -1), 6 units