Question

find the focus and directrix from  this equation of parabola 4y^2- 6x-4y=5

Answer 1

4y² - 6x - 4y = 5
4(y² - y + 1/4 - 1/4) = 6x + 5
4(y - 1/2)² -1 = 6x + 5
4(y - 1/2)² = 6(x + 1)
(y - 1/2)² = 4*3/8(x + 1)
compair with y² = 4ax 
focus of this parabola = (a,0)
directrix =>  x = -a

so focus of given parabola
y - 1/2 = 0
y = 1/2
x + 1 = 3/8
x = -5/8
focus = (-3/8,1/2)
diretrix => x + 1 = -3/8
           x = -11/8