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

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the location of point $P(-6,-6)$ in relation to the circle centered at $C(-1,-3)$ with a radius of 6, we calculate the distance between point $C$ and point $P$. ‖ ‖ 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.⚹◊What is the equation of a circle centered at $C(-1,-3)$ with a radius of 6?⍭ Generate me a similar question◊

Sia