Question

2.2
score: 15/23 answered: 16/23
question 17
write the standard form of the equation of the circle having the given center and containing the given point.
center: (0,1); point: (-1,-2)
question help: written example
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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 and $r$ is the radius. Here, $h = 0$ and $k = 1$, so the equation is $x^{2}+(y - 1)^{2}=r^{2}$.

Step2: Calculate the radius

The radius $r$ is the distance between the center $(0,1)$ and the point $(-1,-2)$. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, we have $r=\sqrt{(-1 - 0)^2+(-2 - 1)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}$.

Step3: Write the final equation

Substitute $r=\sqrt{10}$ into the equation $x^{2}+(y - 1)^{2}=r^{2}$, we get $x^{2}+(y - 1)^{2}=10$.

Answer:

$x^{2}+(y - 1)^{2}=10$