Question

Find the coordinates of the x- and y-intercepts for an ellipse with the equation (x+1)^2/9 + (y-2)^2/8 = 1

Answer 1

Answer:

• x-intercepts: -1±√4.5
• y-intercepts: 2±8/3

Step-by-step explanation:

The x-intercepts are where y = 0.

  (x +1)^2/9 +(0 -2)^2/8 = 1

  (x +1)^2/9 +1/2 = 1 . . . . . simplify a bit

  (x +1)^2 = 9/2 . . . . . . . . .subtract 1/2, multiply by 9; next: square root, add -1

  x = -1 ±√4.5 . . . . . x-intercepts

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The y-intercepts are where x=0.

  (0+1)^2/9 +(y-2)^2/8 = 1

  1/9 + (y -2)^2/8 = 1 . . . . . simplify a bit

  (y -2)^2 = 64/9 . . . . . . . . subtract 1/9, multiply by 8,

  y = 2 ±8/3 . . . . . . take the square root, add 2 . . . . y-intercepts