The book Analytic Geometry And Principles of Algebra was written by author Alexander Ziwet Here you can read free online of Analytic Geometry And Principles of Algebra book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Analytic Geometry And Principles of Algebra a good or bad book?
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Show that an ellipse and hyperbola with common foci are orthogonal. 6. Show that the eccentricity of a hyperbola is equal to the secant of half the angle between the asymptotes. 7. Express the cosine of the angle between the asymptotes of a hyperbola in terms of its eccentricity. 8. Show that the tangents at the vertices of a hyperbola intersect the asymptotes at points on the circle about the center through the foci. 9. Show that the point of contact of a tangent to a hyperbola is the midpoint... between its intersections with the asymptotes. 10. Show that the area of the triangle formed by the asymptotes and any tangent to a hyperbola is constant. 11. Show that the product of the distances from the center of a hyper- bola to the intersections of any tangent with the asymptotes is constant. 12. Show that the tangent to a hyperbola at any point bisects the angle between the focal radii of the point. ( /''^? . | 212 PLANE ANALYTIC GEOMETRY [X, 219 13. As the sum of the focal radii of every point of an ellipse is con- stant ( 204) and the normal bisects the angle between the focal radii ( 216), a sound wave issuing from one focus is reflected by the ellipse to the other focus.
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