**Answer:**

The equation of the parabola in standard form is x = y²/52 + 7·y/26 -

**Step-by-step explanation:**

The standard form of a parabola is a·y² + b·y + c

The focus of the parabola = (-10, -7), the directrix is x = 16, we have;

The coordinate of the focus is given as_F(h + p, k)

Where;

p = 1/(4·a)

The equation of the directrix is x = h - p

Therefore, given that the coordinates of the focus = (-10, -7), we have;

k = -7

Given that the equation of the directrix is x = 16, we have;

h - p = 16...(1)

h + p = -10...(2)

Adding equation (1) and (2), gives;

2·h = 6

h = 6/2 = 3

h = 3

From equation (1), p = h - 16 = 3 - 16 = -13

The general equation of the parabola is (y - k)² = 4·p·(x - h), therefore, substituting the values gives;

(y - (-7))² = 4 × (-13) × (x - 3)

(y + 7)² = -52·(x - 3)

y² + 14·y + 49 = -52·x + 156

x = (y² + 14·y + 49 - 156)/(-52) = (y² + 14·y + 49 - 156)/(-52) = y²/52 + 7·y/26 -107/52