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Consider the problem: Cube equal squares and number. Use al Khayyami's method and identify two conic sections whose intersection yields the solution (give the equations of the curves, and indicate whether they are circles, parabolas, hyperbolas, or ellipses). • Sketch a figure showing the two curves. (The use of GeoGebra is recommended) ● Will the curves always intersect, regardless of the coefficients? ● Suggestion: Treat the problem as x³ = px² + pq², where p, q are lengths, and use the curve 2 Py = = x².

Consider the problem: Cube equal squares and number. Use al Khayyami's method and identify two conic sections whose intersection yields the solution (give the equations of the curves, and indicate whether they are circles, parabolas, hyperbolas, or ellipses). • Sketch a figure showing the two curves. (The use of GeoGebra is recommended) ● Will the curves always intersect, regardless of the coefficients? ● Suggestion: Treat the problem as x³ = px² + pq², where p, q are lengths, and use the curve 2 Py = = x².

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.4: Hyperbolas
Problem 55PS
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Consider the problem: Cube equal squares and number. • Use al Khayyami's method and identify two conic sections whose intersection yields the solution (give the equations of the curves, and indicate whether they are circles, parabolas, hyperbolas, or ellipses). • Sketch a figure showing the two curves. (The use of GeoGebra is recommended) Will the curves always intersect, regardless of the coefficients? Suggestion: Treat the problem as x³ = px² + pq², where p, q are lengths, and use the curve py = x². 2
Transcribed Image Text:Consider the problem: Cube equal squares and number. • Use al Khayyami's method and identify two conic sections whose intersection yields the solution (give the equations of the curves, and indicate whether they are circles, parabolas, hyperbolas, or ellipses). • Sketch a figure showing the two curves. (The use of GeoGebra is recommended) Will the curves always intersect, regardless of the coefficients? Suggestion: Treat the problem as x³ = px² + pq², where p, q are lengths, and use the curve py = x². 2
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