Find the equations of all lines tangent to y = 9–x^2 that pass through the point (1, 12).

The slope of the tangent at a given point can be found by differentiating the given equation and substituting the value of x at the point as such:
y = 9 - x²
dy/dx = -2x; x = 1
dy/dx = -2

For a line with the slope of -2 and passing through point (1 , 12)
y -12 = -2(x - 1)