21. The tangent line in point P(?,?) of the conic section x² - 4xy-y²+2x-4y-8=0 is x-2y-2= 0.Calculate the coordinates of the tangent point. Ans. P(2,0)
21. The tangent line in point P(?,?) of the conic section x² - 4xy-y²+2x-4y-8=0 is x-2y-2= 0.Calculate the coordinates of the tangent point. Ans. P(2,0)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:17. Calculate the real values of m such that the following conic section is degenerated x² - 4 xy + 2 y² - 5 y-m
x+2=0.
Ans. m = +- 3/2 (2)^1/2-5
18. Calculate the double points of the following conic section x² + 4xy+3y²-2xz-4yz+z²=0.
Ans. x = 1, y = 0, z = 1
19. Calculate the double points of the following conic section x² + 2xy + y²-8xz-8yz+16z²=0.
Ans. (x + y - 4 z)² = 0
20. Calculate the tangent line in point P(2.0) of the conic section x² - 4xy-y² + 2x-4y-8=0.
Ans. x-2y-2 z=0
21. The tangent line in point P(?,?) of the conic section x² - 4xy-y²+2x-4y-8-0 is x-2y-2=
0.Calculate the coordinates of the tangent point.
Ans. P(2.0)
22. Calculate the asymptotes of the conic section x² - 4xy-y²+2x-4y-8=0.
Ans.(2x - 4y+2z) + ((11)^1/2 - 4)(-4x-2y-4 z)= 0 and (2x - 4y+2z) + (-(11)^1/2 -4)(-4x-2y-4
z) = 0
23. Calculate the asymptotes of the conic section x² + 2xy + y²-4x-5y+7=0.
Ans. z = 0
24. Calculate the asymptotes of the conic section x² + 2xy-4x=0.
Ans. x = 0 and x+2y-4=0
25. Calculate the asymptotes of the conic section x²-2x = 0.
Ans. x = 00
26. Search the equation of the conic section with asymptotes x=0 and x+2y-41 = 0 and through the point
P(2,1).
Ans.x² + 2xy-41 x + 74= 0
27. Calculate the equation of the system of conic sections with basic points A(1,2); B(2,0); C(-1,1); D(0,3).
Ans. k(-4x² + y² +2xz-7yz+12 z²)+1(-3x² + 4xy+4y²-3xz-18 yz+18 z²) = 0
28. Calculate the equation of the system of conic sections with basic points A(1,2); B(2,0); C(-1,1); C(-1,1) and
such that the line c with equation x+y=0 is the tangent line in point C.
Ans. k(2 x² + 3xy + y² - 4x z- 4y z)+1(-x²-xy+6y²-xz-13yz+6z)=0
29. Calculate the equation of the system of conic sections with basic points A(1,2); A(1,2); B(2,0); B(2,0) and
such that the line a with equation x+y-3 z=0 is the tangent line in point A and b with equation x + 2 y -
2 z=0 is the tangent line in point B.
Ans. k(x+y-3 z)(x+2y-2 z)+1(2x+y-4z)²=0
30. Calculate the basic points of the system with basic conic sections x² + 2xy +7 y² - 5xz-17yz+6z²=0
and-3 x²-4 xy +5y²+3xz-9yz + 6 z²=0.
Ans. (-1,1,1), (1,2,1), (2,0,1), (-1,1,1)
31. Calculate the polar line of P(1,1,1) relative to the conic section -3 x² - 4 xy + 5 y² + 3x z-9yz+6z²=0.
Ans. -7x-3y +6z=0
32. Calculate the polar line of P(1,1,1) relative to the conic section x² - y²-2xz+2yz=0. Ans. 0 = 0
33. Calculate the point C of a polar triangle ABC of the conic section x² + 2xy +7 y²-5xz-17yz+6z²=0
if you know that A(2,1,1) and B(0,15,1).
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