Concept explainers
CONCEPTS
All conics can be described geometrically by using a fixed point
is a__________. If
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Algebra and Trigonometry (MindTap Course List)
- Perihelion and Aphelion The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is closest to the sun is called perihelion, and the point at which it is farthest is called aphelion. These points are the vertices of the orbit. The earth’s distance from the sun is 147,000,000 km at perihelion and 153,000,000 km at aphelion. Find an equation for the earth’s orbit. (Place the origin at the center of the orbit with the sun on the x-axis.)arrow_forward59-62. Graphing Shifting Conics Use a graphing device to graph the conic. 9x2+36=y2+36x+6yarrow_forwardRunning Path Let (0,0) represent a water fountain located in a city park. Each day you run through the park along a path given by x2+y2200x52,500=0 where x and y are measured in meters. (a) What type of conic is your path? Explain. (b) Write the equation of the path in standard form. Sketch the graph of the equation. (c) After you run, you walk to the water fountain. When you stop running at (100,150), how far must you walk for a drink of water?arrow_forward
- Prove that segment FV in Example 7 is the shortest distance between the Earth and the Sun. Hint: Refer to Exercise 63. EXAMPLE 7 The orbit of the Earth is approximately an ellipse, with the sun at one focus. The ratio of c to a called the eccentricity of the ellipse is about 162, and the length of the major axis is approximately 186,000,000 miles. How close does the Earth get to the sun?arrow_forwardProperty of a Hyperbola Use the figure to show that d2d1=2a.arrow_forwardCONCEPTS A Hyperbola is the set of all points in the plane for which the of the distances from two fixed points F1 and F2 is constant. The point F1 and F2 are called the of the hyperbola.arrow_forward
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