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Home » Thus, \( n = 32 \) is the smallest such integer. - Veritas Home Health

Thus, \( n = 32 \) is the smallest such integer. - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Try solving:

📌 From earlier:

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

📌 Only solution is \( x = 0 \), \( y = \pm8 \).

📌 But geometrically: ellipse \( \frac{x^2}{100} + \frac{y^2}{64} = 1 \) has semi-major axis 10 (x), semi-minor 8 (y).

📌 Circle radius 8 — so it touches the ellipse only at \( (0, \pm8) \).

📌 But does it intersect elsewhere? Try \( y=0 \): ellipse \( x = \pm10 \), circle \( x = \pm8 \) — no intersection.

📌 At \( y=0 \), circle has \( x = \pm8 \), ellipse: \( x^2 = 100 \Rightarrow x = \pm10 \), so \( x=8 < 10 \), within ellipse.

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