Question

Math

Posted 3 months ago

```
A circle is centered at $C(-1,-3)$ and has a radius of 6 .
Where does the point $P(-6,-6)$ lie?
Choose 1 answer:
(A) Inside the circle
(B) On the circle
(C) Outside the circle
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 2

The distance formula is $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points

step 3

Substituting the coordinates of $C(-1,-3)$ and $P(-6,-6)$ into the distance formula gives $d = \sqrt{(-6 - (-1))^2 + (-6 - (-3))^2} = \sqrt{(-5)^2 + (-3)^2} = \sqrt{25 + 9} = \sqrt{34}$

step 4

The calculated distance is $\sqrt{34}$, which is approximately 5.83095

step 5

Since the distance from $C$ to $P$ is less than the radius of the circle (6), point $P$ lies inside the circle

1 Answer

A

Key Concept

Distance Formula and Circle Geometry

Explanation

To determine the position of a point relative to a circle, compare the distance from the point to the center of the circle with the radius of the circle. If the distance is less than the radius, the point is inside the circle.

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