Unformatted text preview: becomes y = z 2 . So the equation of the revolution surface is y = x 2 + z 2 : 46. Let P = ( x; y; z ) . The distance from P to the xaxis is p y 2 + z 2 . The distance from P to the yzplane is x . So the equation is p y 2 + z 2 = 2 x; i.e. 4 x 2 & y 2 & z 2 = 0 49. It su¢ ces to check c + 2( b & a ) t = ( b + t ) 2 & ( a + t ) 2 and c & 2( b + a ) t = ( b & t ) 2 & ( a + t ) 2 : This comes immediately from the relation c = b 2 & a 2 : 50. Multiply both sides of x 2 + 2 y 2 & z 2 + 3 x = 1 with 2 ; we have 2 x 2 + 4 y 2 & 2 z 2 + 6 x = 2 : Subtract 2 x 2 + 4 y 2 & 2 z 2 & 5 y = 0 from it, we get 6 x + 5 y = 2 ; which lies in the xyplane. 1...
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 Spring '10
 AB
 Conic section, xy plane

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