Question

multiple choice 10 points where does the point (3, -5) lie in relation to the circle with a center at (-4, -8) and a radius of \\(\sqrt{61}\\)? outside the circle inside the circle on the circle clear my selection previous

Explanation:

Step1: Calculate distance between point and center

Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Here, center $(-4, -8)$, point $(3, -5)$. So $x_1=-4, y_1=-8, x_2=3, y_2=-5$.
$d = \sqrt{(3 - (-4))^2 + (-5 - (-8))^2} = \sqrt{(7)^2 + (3)^2} = \sqrt{49 + 9} = \sqrt{58}$.

Step2: Compare distance with radius

Radius $r = \sqrt{61}$. Since $\sqrt{58} < \sqrt{61}$ (because $58 < 61$), the distance from the point to the center is less than the radius. So the point is inside the circle.

Answer:

Inside the circle (the option: Inside the circle)