Answer #47Handwritten Ans. (221,-11, 14)34. Calculate the center-point of the conic section x² + 2xy +7y²-5xz-17 y z+6z²-0. Ans.(3,2,2)35. What is the general equation of a conic section with the point (0,0,1) as a center-point. Ans. a x² +2b" x y+a'y² +a" z² = 036. Calculate the center-line of the conic section x² + 2xy +7y²-5xz-17yz+ 6 z²= 0 conjugated to thedirection with slope -1.Ans. y=137. Calculate the value of r such that the line x + 2 y + z = 0 is a center-line of the conic section x² + 2xy-y²-rxz+ryz=0.Ans. r = -138. Calculate the direction conjugated to (1.-2.0) relative to the conic section x² + 2xy-y²-4xz+2yz -2 z²= 0.Ans. (1,-2,0) and (1,1/3,0)39. Calculate the center-line conjugated to the center-line 4x-2y+z=0 relative to the conic section x² + 2xy-y²-4xz+2yz -2 z² = 0.Ans. (1,2,0).40. Calculate the axis of the parabola x² + 2xy + y²-4x+2y-6=0.Ans. 2x+2y-1=041. Calculate the focus and the directrix of the parabola x²+2xy + y²-4x+2y-6=0. Ans. -6x+6y+-17 z=042. Find the equation of a line passing through the point (4, 2) and having a slope of 3.Ans. y = 3x - 1043. Calculate the locus of a point P such that the tangent lines from P to the ellipse b²x² + a²y²-a²b² = 0 areorthogonal lines.Ans. x² + y²=a² +6²44. Find the equation of the line that passes through the points (2, 4) and (1, 2).Ans. y = 3x -545. Find the equation of a line through the points (1.2) and (3,1). What is its slope? What is its y intercept?Ans. y=-x/2+5/246. Find distance between points A(3,-4) and B(-1,3)Ans. AB = 8.06247. Find midpoint of a segment with endpoints A(3,-4) and B(-1,3).Ans. M(1, -1/2)48. Find the area of the triangle whose vertices are A(2,4),B(3,-1) and C(-3,3).Ans. K = 1349. Find the centroid of the triangle whose vertices are A(2,4),B(3,-1) and C(-3,3).Ans. xy = (2/3, 2)50. Find the equation of the line determined by A(-2,4) and B(3,-2).Ans. y = -6/5x+8/5

Question

Answer #47Handwritten Ans. (221,-11, 14)34. Calculate the center-point of the conic section x² + 2xy +7y²-5xz-17 y z+6z²-0. Ans.(3,2,2)35. What is the general equation of a conic section with the point (0,0,1) as a center-point. Ans. a x² +2b&#34; x y+a'y² +a&#34; z² = 036. Calculate the center-line of the conic section x² + 2xy +7y²-5xz-17yz+ 6 z²= 0 conjugated to thedirection with slope -1.Ans. y=137. Calculate the value of r such that the line x + 2 y + z = 0 is a center-line of the conic section x² + 2xy-y²-rxz+ryz=0.Ans. r = -138. Calculate the direction conjugated to (1.-2.0) relative to the conic section x² + 2xy-y²-4xz+2yz -2 z²= 0.Ans. (1,-2,0) and (1,1/3,0)39. Calculate the center-line conjugated to the center-line 4x-2y+z=0 relative to the conic section x² + 2xy-y²-4xz+2yz -2 z² = 0.Ans. (1,2,0).40. Calculate the axis of the parabola x² + 2xy + y²-4x+2y-6=0.Ans. 2x+2y-1=041. Calculate the focus and the directrix of the parabola x²+2xy + y²-4x+2y-6=0. Ans. -6x+6y+-17 z=042. Find the equation of a line passing through the point (4, 2) and having a slope of 3.Ans. y = 3x - 1043. Calculate the locus of a point P such that the tangent lines from P to the ellipse b²x² + a²y²-a²b² = 0 areorthogonal lines.Ans. x² + y²=a² +6²44. Find the equation of the line that passes through the points (2, 4) and (1, 2).Ans. y = 3x -545. Find the equation of a line through the points (1.2) and (3,1). What is its slope? What is its y intercept?Ans. y=-x/2+5/246. Find distance between points A(3,-4) and B(-1,3)Ans. AB = 8.06247. Find midpoint of a segment with endpoints A(3,-4) and B(-1,3).Ans. M(1, -1/2)48. Find the area of the triangle whose vertices are A(2,4),B(3,-1) and C(-3,3).Ans. K = 1349. Find the centroid of the triangle whose vertices are A(2,4),B(3,-1) and C(-3,3).Ans. xy = (2/3, 2)50. Find the equation of the line determined by A(-2,4) and B(3,-2).Ans. y = -6/5x+8/5

Accepted Answer

Answered: Image /qna-images/answer/12204fcf-f7b5-42da-9366-277438312895.jpg

47. Find midpoint of a segment with endpoints A(3,-4) and B(−1,3). Ans. M(1, -1/2)