answer all the questions
investigate the coordinates of the intersection point B between the circle and the line, as $r ightarrow \infty$
(a) The line through $A$ and $C$ has equation:
$\mathrm{y}=-\frac{1}{5} \mathrm{x}+2 r$
(b) The x -coordinate of the point B is $\frac{2 r^{2}}{r^{2}+1} imes$
(c) The $y$-coordinate of the point B is $\frac{2 r^{3}}{r^{3}+1} \mathrm{x}$
(d) The limit as $r ightarrow \infty$ of the $x$-coordinate of B is $\infty$ (if your answer is $\infty$, write infinity).
(e) The limit as $r ightarrow \infty$ of the $y$-coordinate of B is $\infty$ $\qquad$ (if your answer is $\infty$, write infinity).

Question

answer all the questions
investigate the coordinates of the intersection point B between the circle and the line, as $r ightarrow \infty$
(a) The line through $A$ and $C$ has equation:
$\mathrm{y}=-\frac{1}{5} \mathrm{x}+2 r$
(b) The x -coordinate of the point B is $\frac{2 r^{2}}{r^{2}+1} 	imes$
(c) The $y$-coordinate of the point B is $\frac{2 r^{3}}{r^{3}+1} \mathrm{x}$
(d) The limit as $r ightarrow \infty$ of the $x$-coordinate of B is $\infty$ (if your answer is $\infty$, write infinity).
(e) The limit as $r ightarrow \infty$ of the $y$-coordinate of B is $\infty$ $\qquad$ (if your answer is $\infty$, write infinity).

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ The equation of the line through points A and C is given by $ y = -\frac{1}{5}x + 2r $. ‖ ‖ step 2 ⋮ The x-coordinate of point B is determined by the limit as $ r \to \infty $ of $ \frac{2r^2}{r^2 + 1} $, which simplifies to $ 2 $. ‖ ‖ step 3 ⋮ The y-coordinate of point B is determined by the limit as $ r \to \infty $ of $ \frac{2r^3}{r^3 + 1} $, which also simplifies to $ 2 $. ‖ ‖ step 4 ⋮ As $ r \to \infty $, the limit of the x-coordinate of B approaches $ 2 $. ‖ ‖ step 5 ⋮ As $ r \to \infty $, the limit of the y-coordinate of B approaches $ 2 $. ‖ ∻[question number] Answer∻ ***A*** ∻Key Concept∻ ⚹Limits and Intersection Points⚹ ∻Explanation∻ ⚹Understanding how to find the limits of coordinates as a variable approaches infinity is crucial in analyzing the behavior of functions and their intersections.⚹◊What is the geometric interpretation of the intersection point B in terms of the properties of the circle and the line as $r$ increases?⍭ Generate me a similar question◊

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