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4) The lemniscate curve (x? + y²)² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted that it is "shaped like a figure 8, or a knot, or the bow of a ribbon." Find the coordinates of the four points at which the tangent line is horizontal.

4) The lemniscate curve (x? + y²)² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted that it is "shaped like a figure 8, or a knot, or the bow of a ribbon." Find the coordinates of the four points at which the tangent line is horizontal.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4) The lemniscate curve (x² + y²)² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted that it is "shaped like a figure 8, or a knot, or - the bow of a ribbon." Find the coordinates of the four points at which the tangent line is horizontal. y 1 1 FIGURE 9 Lemniscate curve: (x² + y²)² = 4(x² – y²). -
Transcribed Image Text:4) The lemniscate curve (x² + y²)² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted that it is "shaped like a figure 8, or a knot, or - the bow of a ribbon." Find the coordinates of the four points at which the tangent line is horizontal. y 1 1 FIGURE 9 Lemniscate curve: (x² + y²)² = 4(x² – y²). -
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