1. ## 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?

2. Hi struck
Originally Posted by struck
y = 1/2x - 3/2 - 2
2y = x - 4
I think you want to check this once again ^^

To find the point where the normal meets the curve again, subs. the equation of the normal to the equation of the curve.

3. Originally Posted by songoku
Hi struck

I think you want to check this once again ^^

To find the point where the normal meets the curve again, subs. the equation of the normal to the equation of the curve.
Oh yea, it should be 2y = x - 7... But I still don't understand how to solve the next part. How do you sub. the equation of the normal to the equation of the curve

4. Hi struck

Equation of the curve : 4x^2 - 3y^2 = 24
Equation of normal : 2y = x - 7 ---------------> x = 2y + 7

Because the curve and the normal intersect :
4x^2 - 3y^2 = 24
4 (2y+7)^2 - 3y^2 = 24 --------> solve for y