Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in...
Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation 2x2 + 12xy – 3y2 – 50 = 0. Identify the resulting rotated conic and give its equation in the new coordinate system. Selected Answer: Ellipse; 9(x')? +967')2-50=0 b.
Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 5x² - 4xy + 5y² - 81 - 0 (a) Identify the resulting rotated conic. hyperbola O parabola O ellipse (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 5x2 - 4xy + 5y2 - 16 = 0 (a) Identify the resulting rotated conic, O hyperbola O parabola O ellipse (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 6x2 - 2xy + 6y2 - 25 = 0 (a) Identify the resulting rotated conic. O parabola O hyperbola ellipse (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.) Need Help? Read It Talk to a Tutor
1 points Use the Principal Axes Theorem to perform a rotation of ases to eliminate the xy-term in the quadratic equation 22° +12y – 3y-50 0, identify the resulting rotated conic and give is op the new coordinate system a Ellipse: -9(x"}+967"-50=0 Ellipse, 7(x")+6019-50 - 0 Hyperbola: -7x"}+6("2 - 50 = 0 d. Ellipse;9(x")+909")2-50 - 0 e Hyperbola: 7(x") - 609") - 50 = 0
Perform a rotation of axes to eliminate the xy-term. (Use X2 and y2 for the rotated coordinates.) x2 + 2xy + y2 + 2x - 2y = 0 Sketch the graph of the conic. - 4 - 2 2 4 - 4 -2 2 4 LUX - 4 - 2 24 -4 -2 4
2. (15) Give the standard form equation of the parabola with vertex = (1,2) and focus = (3, 2) b. the ellipse with center (-1,3), a focus at (-1,7) and a major axis point (1,8) c. the hyperbola with foci at (3,3), (3,-7) and vertices at (3,1), (3,-5). 3. (12) Identify the conic section and complete the square to give the standard equation given 3x2-10y +36x -20y+38 0 is 3 (24) Given the parametric equations x-Y-2, y-t,-2 4· a. Sketch...
conic section
Now consider the conic represented by the equation xyy-22x +2/2y-0. For this equation, it is more difficult to wrte t in the form -h. 1 because of the xyterm. When a conic with equaticon difficult to write it in the formk - 1 because of the xy term. When a conic with equation ax' + bxy + cy'+dx ey+-0 is rotated about an angle 6, where cot 20-converting from basis B: # {( 1, 0), (0, 1)) to...
Question 15 O pts Each equation below represents a conic section. Write the name of the corresponding type of conic. Explain how you know if it is a circle, ellipse, hyperbola or parabola. a) 1 25 9 b) y2 + 6y + x - 6 = 0 c) x² + y2 100 a) ? 9 b) y? – 6y + 2 – 6 – 0 c).x2 + y2 100
6. Find a basis for the subspace of R3 spanned by S (42,30,54), (14,10, 18),(7,5,6)). 7. Given that [xlg [4,5,3]', the coordinate matrix of x relative to a (nonstandard) basis B((,1,0(1,0,1),(0,0,0)). Find the coordinate vector of x relative to the standard basis in R3 8. Find the coordinate matrix of x=(-3,28,6) in Rs relative to the basis B=((3,8,0),(5,0,11),( 1,5,7), 9. Find the transition matrix from B ((1,7),(-2, -2))to B'- ((-28,0),(-4,4)) 10 Perform a rotation of axes to eliminate the xy-term,...