1. A comet's path (as it approaches the sun) can be modeled by one branch of hyperbola 1600 = 1 where the sun is at the focus of that part of hyperbola. Each unit of the coordinate system 39204 represent 1 million miles. Find the coordinates of the sun (assuming it is at the focus with non- negative coordinates). How close does the comet come to the sun? 2. The towers of a bridge connecting two cities are 2560 meters apart and rise 320 meters above the road. The cable between the towers has the shape of a parabola and the cable just touches the side of the road midway between the towers. What is the height of the cable 400 meters from a tower? Round to the nearest meter.

1. A comet's path (as it approaches the sun) can be modeled by one branch of hyperbola 1600 = 1 where the sun is at the focus of that part of hyperbola. Each unit of the coordinate system 39204 represent 1 million miles. Find the coordinates of the sun (assuming it is at the focus with non- negative coordinates). How close does the comet come to the sun? 2. The towers of a bridge connecting two cities are 2560 meters apart and rise 320 meters above the road. The cable between the towers has the shape of a parabola and the cable just touches the side of the road midway between the towers. What is the height of the cable 400 meters from a tower? Round to the nearest meter.

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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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.

Question

solve the following problems involving conic sections.

(please make the solutions easier to understand and study)

1.
A comet's path (as it approaches the sun) can be modeled by one branch of hyperbola
1600
= 1 where the sun is at the focus of that part of hyperbola. Each unit of the coordinate system
%3D
39204
represent 1 million miles. Find the coordinates of the sun (assuming it is at the focus with non-
negative coordinates). How close does the comet come to the sun?
2.
The towers of a bridge connecting two cities are 2560 meters apart and rise 320 meters above
the road. The cable between the towers has the shape of a parabola and the cable just touches the
side of the road midway between the towers. What is the height of the cable 400 meters from a
tower? Round to the nearest meter.

Curve that is obtained by the intersection of the surface of a cone with a plane. The three types of conic sections are parabolas, ellipses, and hyperbolas. The main features of conic sections are focus, eccentricity, and directrix. The other parameters are principal axis, linear eccentricity, latus rectum, focal parameter, and major and minor axis.

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