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Unformatted text preview: Section 1.1
4 3 0 0 4 . 3 5 51. The radius through (3, 4) has slope The tangent line is tangent to this radius, so its slope is y y y
3 (x 4 3 x 4 3 x 4 1 4/3 3 . We seek the line of slope 4 3 that passes through (3, 4). 4 3)
9 4 25 4 4 4 52. (a) The equation for line L can be written as y y
A x B B (x A C , so its slope is B A . The perpendicular line has slope B 1 A/B B and passes through (a, b), so its equation is A a)
B A b. a) b ABb B2)x x b for y in the equation for line L gives: C AC B2 a
B2 a (b) Substituting (x Ax Ax
2 B
2 B (x A a) a) B (x (A2 AC ABb AC ABb A2 B 2 Substituting the expression for x in the equation for line L gives: A By By By y
B2 a AC ABb By C A2 B 2 A(B2a AC ABb) C(A2 B2) 2 2 A B A2 B 2 2 2 2 2 AB a A C A Bb A C B2C A2 B2 A2Bb A2 b B2C AB2a A2 B2 BC ABa A2 B2 B2a A AC
2 The coordinates of Q are (c) Distance (x
B2a B2a AC A(C A2 ABb A2b B
2 , BC ABa . A2 B2 a)2 (y b)2
2 AC ABb A2 B 2 AC a A2 b B2) 2 BC ABa A2 B 2 A2b BC 2 b
ABa b(A2 A2 B2 B2 ) 2 ABb a(A2 A2 B2 BC B(C A Bb A 2 a 2 B2 A
2 ABa B2b 2 B2 A
2 Bb B2 Aa) 2 Aa A2 B2 Bb) 2 A2(C Aa Bb)2 (A2 B2)2 (A2 (C A C Aa A B2)(C Aa (A2 B2)2 Aa
2 B2(C Aa Bb)2 (A2 B2)2 Bb)2 Bb)2 B
2 Aa A2 Bb
2 Bb B2 C B
2 ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN
 Slope

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