Answer:

x² – (y-1)²/4 = 1

Step-by-step explanation:

4x²-y²+2y-5 = 0

4x²-y²+2y = 5

4(x²) + -1(y²-2y) = 5

4(x²) + -1(y²-2y+1) = 5+(-1)

4(x²) – (y²-2y+1) = 5 – 1

4(x²) – (y+1)² = 4

Divide both sides by 4

4(x²)/4 – (y-1)²/4 = 4/4

x² – (y–1)²/4 = 1