What does tangent to x = -10 mean?

I assume that you need to find the equation of the ellipse.

The vertex and focus are horizontally aligned, so the ellipse is horizontal.

The center lies on the x-axis.

x = -10 is the vertical line that passes through (-10, 0). Since it is tangent to the ellipse, the point of tangency must be one of the vertices. So, the second vertex is (-10, 0).

The center is exactly halfway between vertices, at (0, 0).

General equation of a horizontal ellipse:

(x - h)²/a² + (y - k)²/b² = 1

where

(h, k) is the center

(h±a, k) are the vertices

(h±c, k) are the foci, where c² = a² - b²

Use your data to determine h, k, a, and b.

center (h, k) = (0, 0)

h = 0

k = 0

vertices (h±a, k) = (0±10, 0)

a = 10

focus (0±c, 0) = (8, 0)

c = 8

c² = a² - b²

64 = 100 - b²

b² = 36

The equation of the ellipse is x²/100 + y²/36 = 1