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Find the foci vertices and center of the new ellipse

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Reference no: EM132323130

Assignment - Solve the problems and write the solution in LaTeX:

Problem 1 - The parabola y2 = 8x is shifted down 2 units and right 1 unit to generate the parabola (y + 2)2 = 8(x - 1).

a. Find the new parabola's vertex, focus, and directrix.

b. Plot the new vertex, focus, and directrix, and sketch in the parabola.

Problem 2 - The parabola x2 = -4y is shifted left 1 unit and up 3 units to generate the parabola (x + 1)2 = -4(y - 3).

a. Find the new parabola's vertex, focus, and directrix.

b. Plot the new vertex, focus, and directrix, and sketch in the parabola.

Problem 3 - The ellipse (x2/16) + (y2/9) = 1 is shifted 4 units to the right and 3 units up to generate the ellipse

(x - 4)2/16 + (y - 3)2/9 = 1.

a. Find the foci, vertices, and center of the new ellipse.

b. Plot the new foci, vertices, and center, and sketch in the new ellipse.

Problem 4 - The ellipse (x2/9) + (y2/25) = 1 is shifted 3 units to the left and 2 units down to generate the ellipse

(x + 3)2/9 + (y + 2)2/25 = 1.

a. Find the foci, vertices, and center of the new ellipse.

b. Plot the new foci, vertices, and center, and sketch in the new ellipse.

Problem 5 - The hyperbola (x2/16) - (y2/9) = 1 is shifted 2 units to the right to generate the hyperbola

(x - 2)2/16 - y2/9 = 1.

a. Find the center, foci, vertices, and asymptotes of the new hyperbola.

h. Plot the new center, foci, vertices, and asymptotes, and sketch in the hyperbola.

Problem 6 - The hyperbola (y2/4) - (x2/5) = 1 is shifted 2 units down to generate the hyperbola

(y + 2)2/4 - x2/5 = 1.

a. Find the center, foci, vertices, and asymptotes of the new hyperbola.

h. Plot the new center, foci, vertices, and asymptotes, and sketch in the hyperbola.

Problems 7-10 - give equations for parabolas and tell how many units up or down and to the right or left each parabola is to be shifted. Find an equation for the new parabola, and find the new vertex, focus, and directrix.

7. y2 = 4x, left 2, down 3

8. y2 = -12x, right 4, up 3

9. x2 = 8y, right 1, down 7

10. x2 = 6y, left 3, down 2.

Reference no: EM132323130

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