Question

2.2 score: 6/13 answered: 6/13 question 7 find the equation of the circle with center at (-3,4) and passes through the point (6,4). enter your answer as an equation. example: y=3x^2+1, 2+x+y=3 be sure your variables match those in the question

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius. Here, $h=-3$ and $k = 4$, so the equation is $(x + 3)^2+(y - 4)^2=r^2$.

Step2: Calculate the radius

The radius $r$ is the distance between the center $(-3,4)$ and the point $(6,4)$ on the circle. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, we have $x_1=-3,y_1 = 4,x_2=6,y_2 = 4$. Then $r=\sqrt{(6+3)^2+(4 - 4)^2}=\sqrt{9^2+0^2}=9$.

Step3: Write the circle - equation

Substitute $r = 9$ into the equation $(x + 3)^2+(y - 4)^2=r^2$. We get $(x + 3)^2+(y - 4)^2=81$.

Answer:

$(x + 3)^2+(y - 4)^2=81$