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Home » Since \( f(3) = g(3) \), we have: - Sterling Industries

Since \( f(3) = g(3) \), we have: - Sterling Industries

📅 April 15, 2026 👤 scraface

Apr 15, 2026

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📌 x^2\left( \frac{1}{100} - \frac{1}{64} \right) = 0

📌 x^2 \left( \frac{64 - 100}{6400} \right) = 0 \Rightarrow x^2(-36/6400) = 0

📌 So \( x = 0 \) is the only solution — but this implies the circle is tangent at \( (0, \pm8) \)? Let's verify:

📌 At \( x = 0 \): \( y^2 = 64 \), so \( y = \pm8 \).

📌 Check in ellipse: \( 0 + \frac{64}{64} = 1 \) — yes.

📌 Now check if other intersections exist:

📌 The circle has radius 8, ellipse semi-minor axis is 8 — so the circle touches the ellipse at the top and bottom.

📌 But does it intersect in more points? No — since the circle lies entirely on or inside the ellipse in \( y \), but at \( x=0 \), both are 1.

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