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Home » Now compute \( (x + 2y)^2 \): - AMAZONAWS

Now compute \( (x + 2y)^2 \): - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 A satellite orbits Earth along a path modeled by the ellipse \( \frac{x^2}{100} + \frac{y^2}{64} = 1 \). If the satellite’s signal covers a circular region of radius 8 units centered at the origin, what is the maximum number of points from the orbit that the signal reaches (accounting for intersections)?

📌 Determine where the ellipse intersects the circle \( x^2 + y^2 = 64 \).

📌 Substitute \( y^2 = 64 - x^2 \) into the ellipse equation:

📌 \frac{x^2}{100} + \frac{64 - x^2}{64} = 1

📌 Multiply through by \( 6400 \) (LCM of 100 and 64):

📌 64x^2 + 100(64 - x^2) = 6400

📌 64x^2 + 6400 - 100x^2 = 6400

📌 -36x^2 = 0 \Rightarrow x^2 = 0

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