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Home » The total number of positive divisors is: - IQnection

The total number of positive divisors is: - IQnection

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 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.

📌 Actually, the circle is inscribed: at \( x=0 \), both have \( y = \pm8 \), and for \( |x| > 0 \), ellipse allows larger \( x \), but circle restricts \( x^2 + y^2 = 64 \), so maximum \( y \) is bounded.

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