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Pre-Calc Homework Solutions 5

# Pre-Calc Homework Solutions 5 - Section 1.1 4 3 0 0 4 3 5...

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51. The radius through (3, 4) has slope } 4 3 2 2 0 0 } 5 } 4 3 } . The tangent line is tangent to this radius, so its slope is } 2 4/3 1 } 5 2 } 3 4 } . We seek the line of slope 2 } 3 4 } that passes through (3, 4). y 5 2 } 3 4 } ( x 2 3) 1 4 y 5 2 } 3 4 } x 1 } 9 4 } 1 4 y 5 2 } 3 4 } x 1 } 2 4 5 } 52. (a) The equation for line L can be written as y 5 2 } A B } x 1 } C B } , so its slope is 2 } A B } . The perpendicular line has slope } 2 2 A 1 / B } 5 } B A } and passes through ( a , b ), so its equation is y 5 } B A } ( x 2 a ) 1 b . (b) Substituting } B A } ( x 2 a ) 1 b for y in the equation for line L gives: Ax 1 B 3 } B A } ( x 2 a ) 1 b 4 5 C A 2 x 1 B 2 ( x 2 a ) 1 ABb 5 AC ( A 2 1 B 2 ) x 5 B 2 a 1 AC 2 ABb x 5 } B 2 a 1 A 2 A 1 C B 2 2 ABb } Substituting the expression for x in the equation for line L gives: A 1 } B 2 a 1 A 2 A 1 C B 2 2 ABb } 2 1 By 5 C By 5 1 } C A ( A 2 2 1 1 B B 2 2 ) } By 5 By 5 y 5 The coordinates of Q are 1 , 2 . (c) Distance 5 ˇ ( x w 2 w a w ) 2 w 1 w ( w y w 2 w b w ) 2 w 5 ! 1 } B § 2 a § 1 A § 2 A § 1 C § B 2 § 2 § A § B § b } § 2 § a § 2 2 § 1 § 1 § } A § 2 b § 1 A § 2 B § 1 C § B 2 § 2 § A § B § a } § 2 § b § 2 2 § 5 ! 1 § §§ 2 2 § 1 § 1 § §§ 2 2 § 5 ! 1 } A § C § 2 § A § 2 A § 1 B § b B § 2 2 § A § 2 a } § 2 2 § 1 § 1 § } B § C § 2 § A § 2 A § 1 B § a B § 2 2 § B § 2 b } § 2 2 § 5 ! 1 } A § ( C § A 2 § 2 § B 1 § b B § 2 2 § A § a ) } § 2 2 § 1 § 1 § } B § ( C § A 2 § 2 § A 1 § a B § 2 2 § B § b ) } § 2 2 § 5 ! §§ 1 § § §§ 5 ! §§ 5 ! } ( C § 2 § A § 2 A § 1 a § 2 B § 2 B § b § ) 2 } § 5
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