Step-by-step explanation:
16x² − 9y² − 64x − 90y − 305 = 0
Group the x's together and the y's together.
16x² − 64x − 9y² − 90y = 305
Factor:
16 (x² − 4x) − 9 (y² − 10y) = 305
Complete the squares:
16 (x² − 4x + 4) − 9 (y² − 10y + 25) = 305 + 16(4) − 9(25)
16 (x − 2)² − 9 (y − 5)² = 144
Divide by 144:
(x − 2)²/9 − (y − 5)²/16 = 1
This is a horizontal hyperbola (the x term is positive).
The center is (2, 5).
The vertices are (-1, 5) and (5, 5) (plug in y = 5).
The slant asymptotes are y = ±16/9 (x − 2) + 5.
Graph:
desmos.com/calculator/tkcwnlb1ga
