Given the following equation for a hyperbola: 16x^2-9y^2-64x-90y-305=0Write the equation in standard form and graph it.(label the center vertices and slanted asymptotes)(Show details please!)
Accepted Solution
A:
Step-by-step explanation:16x² − 9y² − 64x − 90y − 305 = 0Group the x's together and the y's together.16x² − 64x − 9y² − 90y = 305Factor:16 (x² − 4x) − 9 (y² − 10y) = 305Complete the squares:16 (x² − 4x + 4) − 9 (y² − 10y + 25) = 305 + 16(4) − 9(25)16 (x − 2)² − 9 (y − 5)² = 144Divide by 144:(x − 2)²/9 − (y − 5)²/16 = 1This 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