Implicit equation issue..

4. Differentiate the implicit equation of the hyperbola 4x^2 - 3y^2 = 24 to find the equation of the normal at the point (3, -2). Find the y-coordinate of the point where the normal meets the curve again.

Differentiating:

=> 8x - 6y dy/dx = 0

=> 8x = 6y dy/dx

=> dy/dx = 8x / 6y

At (3, -2), the gradient of normal is 1 / m, where gradient = 24 / -12 = -2 :

m = 1/2

So the equation of the normal is:

y + 2 = 1/2(x - 3)

y = 1/2x - 3/2 - 2

2y = x - 4

I don't know where to go from here. How to find the y-coordinate of the point where the normal meets the curve again?