+128475 Rearrange as
16y^2 - 2y - 4x^2 = 3 complete the square on y
16 (y^2 - 1/8y + 1/256) - 4x^2 = 3 + 1/16
16 ( y - 1/16)^2 - 4x^2 = 49/16 divide both sides by 49/16
16 ( y -1/16)^2 / ( 49/16) - 4x^2 / (49/16) = 1 and we can write
(y - 1/16)^2 / (49/256) - x^2 / ( 49/64) = 1
a^2 = 49/256 a = 7/16
b^2 = 49/64 b = 7 / 8
The center is ( 0, 1/16)
The slope is a / b = (7/16) / ( 7/8) = 8/16 =1/2
Equation of the asymptote with positive slope :
y =(1/2)x + 1/16
Here's a graph that confirms this : https://www.desmos.com/calculator/9dzysghfat
