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?