Answer #31 handwritten

17. Calculate the real values of m such that the following conic section is degenerated x - 4 xy + 2 y: - 5 y - m x +2 =0. Ans. m = +- 3/2 (2)1/2-5 18. Calculate the double points of the following conic section x# + 4 xy + 3 y: - 2x z - 4 y z + 23=0. Ans. x = 1, y = 0, z=1 19. Calculate the double points of the following conic section x" + 2x y + y' - 8 xz - 8 yz+ 16 z*=0. Ans. (x + y - 4z) =0 20. Calculate the tangent line in point P(2,0) of the conic section x - 4 x y - y' + 2x - 4 y - 8 =0. Ans. x - 2 y - 2z=0 21. The tangent line in point P(?,?) of the conic section x - 4 x y - y' + 2 x - 4 y - 8 =0 is x- 2y - 2= O.Calculate the coordinates of the tangent point. Ans. P(2,0) 22. Calculate the asymptotes of the conic section x* - 4 x y - y# + 2x - 4y - 8= 0. Ans.(2 x - 4 y + 2z) + ((11)*1/2 - 4)(-4 x - 2 y - 4 z)=0 and (2 x - 4 y +2z) +(-(11)^1/2 - 4)(-4 x - 2y - 4 z) =0 23. Calculate the asymptotes of the conic section x* + 2 xy + y' - 4 x - 5 y + 7 =0. Ans. z = 0 24. Calculate the asymptotes of the conic section x* + 2xy - 4 x = 0. Ans. x = 0 and x + 2 y - 4=0 25. Calculate the asymptotes of the conic section x*- 2 x = 0. Ans. X = 00 26. Search the equation of the conic section with asymptotes x = 0 and x + 2 y - 41 = 0 and through the point P(2, 1). Ans.x- + 2 x y - 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(-4 x3 + y: + 2xz - 7yz+ 12 z)+1(-3 x# +4xy +4 y: - 3xZ - 18 y z+ 18 z') =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 x + 3 xy+ y' - 4xz - 4yz)+1(-x - xy+6y - xz- 13 yz+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 + 2 y - 2z) +1(2x + y -4z)=0 30. Calculate the basic points of the system with basic conic sections x' + 2 xy + 7 y - 5 xz - 17 yz+ 62=0 and -3 x - 4 x y + 5 y' + 3xz-9yz+62*=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 x - 4 xy + 5 y'+ 3xz - 9yz+6z*=0. Ans. -7 x - 3y +6z=0 32. Calculate the polar line of P(1, 1,1) relative to the conic section x - y' - 2 x z + 2 yz=0. Ans. 0=0 33. Calculate the point C of a polar triangle ABC of the conic section x* + 2 xy + 7 y' - 5 x z - 17 y z+62*=0 if you know that A(2,1,1) and B(0,15,1)