Algebra.Com's Answer #840559 by ikleyn(52790)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A comet's path as it approaches the sun can be modeled by one branchof hyperbola y²/1225 - x²/40401 = 1,
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document.write( "where the sun is at the focus of that path of the hyperbola. Each unit of the coordinate system
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document.write( "is 1 million kilometers. Find the coordinates of the sun and how close the comet come to the sun.
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document.write( "One vertex of the hyperbola is the point V1 = (x,y) = (0, ) = (0,35).\r\n" );
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document.write( "The other vertex of the hyperbola is V2 = (x,y) = (0,-) = (0,-35).\r\n" );
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document.write( "The real axis of the hyperbola (= the transverse axis) in this coordinate system is vertical segment [V1,V2].\r\n" );
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document.write( "The foci are the points F1 = (0, = (0,204.0245) and F2 = (0,-204.0245).\r\n" );
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document.write( "By identifying the position of the sun with the focus F1, we can say that the position of the sun is \r\n" );
document.write( "F1 = (0,204.0245), or 204.0245 million kilometers along the y-axis.\r\n" );
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document.write( "Then the position of the comet, closest to the sun, is at vertex V1 = (0,35),\r\n" );
document.write( "and the smallest distance the comet from the sun is 204.0245-35 = 169.0245 million kilometers.\r\n" );
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document.write( "ANSWER. Coordinates of the sun are x= 0, y= 204.0245 million kilometers.\r\n" );
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document.write( " The smallest distance of the comet from the sun is 169.0245 million kilometers.\r\n" );
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document.write( "Solved.\r
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document.write( "For references, see this Internet site \r
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document.write( "https://courses.lumenlearning.com/waymakercollegealgebra/chapter/equations-of-hyperbolas/\r
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