Questions: Given a circle with center (-1,-7) and radius √5, (a) Write an equation of the circle in standard form. (b) Graph the circle. Part 1 of 2 (a) An equation of the circle in standard form is .

Given a circle with center (-1,-7) and radius √5,
(a) Write an equation of the circle in standard form.
(b) Graph the circle.

Part 1 of 2
(a) An equation of the circle in standard form is .

Transcript text: Given a circle with center $(-1,-7)$ and radius $\sqrt{5}$, (a) Write an equation of the circle in standard form. (b) Graph the circle. Part 1 of 2 (a) An equation of the circle in standard form is $\square$ .

Solution

Solution Steps

Step 1: Identify the center and radius of the circle

The center of the circle is given as $(-1, -7)$ and the radius is $\sqrt{5}$.

Step 2: Write the equation of the circle in standard form

The standard form of the equation of a circle with center $(h, k)$ and radius $r$ is: \[ (x - h)^2 + (y - k)^2 = r^2 \] Substituting $h = -1$, $k = -7$, and $r = \sqrt{5}$: \[ (x + 1)^2 + (y + 7)^2 = (\sqrt{5})^2 \] \[ (x + 1)^2 + (y + 7)^2 = 5 \]

Final Answer

(a) An equation of the circle in standard form is $(x + 1)^2 + (y + 7)^2 = 5$.

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