Question

given a circle where the center is (-2, -4) and another point on the circle is (-10, -10), (a) write an equation of the circle in standard form. (b) graph the circle. part: 0 / 4 part 1 of 4 the select of the circle is the distance between a point on the circle and the center.

Explanation:

Step1: Identify the missing term

The distance from a circle's center to any point on the circle is defined as its radius.

Step2: Calculate radius length

Use distance formula: $r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Substitute $(-2,-4)$ and $(-10,-10)$:
$r=\sqrt{(-10-(-2))^2+(-10-(-4))^2}=\sqrt{(-8)^2+(-6)^2}=\sqrt{64+36}=\sqrt{100}=10$

Step3: Write standard circle equation

Standard form: $(x-h)^2+(y-k)^2=r^2$, where $(h,k)=(-2,-4)$, $r=10$
$(x-(-2))^2+(y-(-4))^2=10^2$
Simplify: $(x+2)^2+(y+4)^2=100$

Step4: Describe graphing the circle

Plot center $(-2,-4)$, mark points 10 units up/down/left/right from center, then draw a smooth circle through these points.

Answer:

Part 1 of 4: radius
(a) $(x+2)^2+(y+4)^2=100$
(b) To graph:

1. Plot the center at $(-2, -4)$ on a coordinate plane.
2. Plot 4 key points: 10 units right $(-2+10, -4)=(8, -4)$, 10 units left $(-2-10, -4)=(-12, -4)$, 10 units up $(-2, -4+10)=(-2, 6)$, 10 units down $(-2, -4-10)=(-2, -14)$.
3. Draw a smooth, closed circle connecting these 4 points, centered at $(-2, -4)$.