Answer :
Explanation :
In order to figure out where does point V stands ,we are required to find the radius of the circle which is equivalent to the distance between point A and point M and then compare the distance between the centre and point V.
now, we find the distance from the centre to point V
since the distance between the centre and point V is less than the radius of the circle thus, it exists inside of the circle .
Answer:
Inside the circle
Step-by-step explanation:
To determine the position of point V relative to the circle centered at A(-5, -8) with point M(-1,-3) lying on it, we can use the distance formula.
[tex]\boxed{\begin{array}{l}\underline{\sf Distance \;Formula}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\;d\;\textsf{is the distance between two points.} \\\phantom{ww}\bullet\;\;\textsf{$(x_1,y_1)$ and $(x_2,y_2)$ are the two points.}\end{array}}[/tex]
The distance between the center of the circle, A(-5, -8), and point M(-1,-3) is equal to the radius (r) of the circle:
[tex]r=\sqrt{(x_M-x_A)^2+(y_M-y_A)^2}\\\\r=\sqrt{(-1 - (-5))^2 + (-3 - (-8))^2}\\\\r= \sqrt{4^2 + 5^2} \\\\r= \sqrt{16 + 25} \\\\r= \sqrt{41}[/tex]
Therefore, the radius of the circle is √41.
Now, find the distance between the center of the circle, A(-5, -8), and point V(-11, -6):
[tex]d=\sqrt{(x_V-x_A)^2+(y_V-y_A)^2}\\\\d=\sqrt{(-11 - (-5))^2 + (-6 - (-8))^2} \\\\d= \sqrt{(-6)^2 + 2^2} \\\\d= \sqrt{36 + 4} \\\\d= \sqrt{40}[/tex]
Since √40 is less than √41, the distance between point V and the center of the circle is less than the radius of the circle. Therefore, point V lies:
[tex]\Large\boxed{\textsf{Inside the circle}}[/tex]
