Question

Write the equation of the circle given the following information center: (-12,7)point of the circle:(-12,9)

Answer 1

Hello!

First, we have to find the radius of this circumference. We can obtain it using the formula to calculate the distance between two points, look:

$\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(-12-(-12))^2+(9-7)^2} \\ d=\sqrt{(-12+12)^2+(2)^2} \\ d=\sqrt{0+4} \\ d=\sqrt{4} \\ d=2 \end{gathered}$

So, we know that:

• Center,: (-12, 7)

,

• Radius,: 2

To write the equation of the circle, we must use the formula below:

$(x-x_C)^2+(y-y_C)^2=r^2$

So, let's replace it with the values in the topics:

$\begin{gathered} (x--12)^2+(y-7)^2=2^2 \\ (x+12)^2+(y-7)^2=4 \end{gathered}$

Look at it in the cartesian point below:

Answer:

(x+12)² + (y -7)² = 4