Answer:
32(x-1)²/33 +12(y-1/2)²/11 = 1
Step-by-step explanation:
The equation of the ellipse is:
8x² + 9y² - 16x - 9y + 2 = 0
First, let's rewrite the expression as:
(8x² - 16x) + (9y² - 9y) + 2 = 0
(8x² - 16x) + (9y² - 9y) + 2 - 2 = 0 - 2
(8x² - 16x) + (9y² - 9y) = -2
Now, we need to complete the squares, so we will add 8 and 9/4 to both sides to get:
(8x² - 16x + 8) + (9y² - 9y + 9/4) = -2 + 8 + 9/4
8(x² - 2x + 1) + 9(y² - y + 1/4) = 33/4
8(x - 1)² + 9(y - 1/2)² = 33/4
Finally, multiply by 4 and divide by 33 to get:
4(8)(x-1)² + 4(9)(y - 1/2)² = 4(33/4)
32(x-1)² +36(y-1/2)² = 33
32(x-1)²/33 +36(y-1/2)²/33 = 33/33
32(x-1)²/33 +12(y-1/2)²/11 = 1
Therefore, the answer is:
32(x-1)²/33 +12(y-1/2)²/11 = 1