What is the equation of a parabola with (−1, −3) as its focus and y = 1 as its directrix? enter the equation in the box.

We are asked to solve for the equation of a parabola given that its focus is (-1, -3) and its directrix is y=1. We can solve this problem by using the equation in solving distance between two points such as shown below:
d² = (x2-x1)² + (y2-y1)²
where d is the directrix y = 1
(y-1)² = (x+1)² + (y+3)²
Perform square root on both sides such as:
√ (y-1)² = √((x+1)² + (y+3)²)
(y-1)² = (x+1)² + (y+3)²
y² - 2y +1 = x² + 2x + 1 + y² + 6y +9
y²-y² -2y -6y +1 -9 = x²+2x+1
-8y-8 = x² + 2x +1
-8y -8= x²+2x + 1
y = ((x+1)² + 8 ) / (-8)
y = - (x+1)²/8  - 1

The answer is y = -(x+1)²/8   - 1.