# Thread: Parametric equations and curve

1. ## Parametric equations and curve

Not sure if I am posting this in right section. I do not know which section of maths does parametric equations belong to.

(a) Find the equation of the normal to the hyperbola x = 4t, y = 4 / t at the point (8,2)

I found the equation to be:

y = 4x - 30

(b) Find the coordinates of the point where this normal crosses the curve again

Now I have no idea how to solve (b)

2. Originally Posted by struck
Not sure if I am posting this in right section. I do not know which section of maths does parametric equations belong to.

(a) Find the equation of the normal to the hyperbola x = 4t, y = 4 / t at the point (8,2)

I found the equation to be:

y = 4x - 30

(b) Find the coordinates of the point where this normal crosses the curve again

Now I have no idea how to solve (b)
Eliminating the parameter we get the equation of the hyperbola as:

$\displaystyle xy=16$

Sub $\displaystyle y = 4x - 30$

$\displaystyle x(4x-30)=16$

$\displaystyle x(2x-15)=8$

$\displaystyle 2x^2-15x-8=0$

$\displaystyle 2x^2-16x+x-8=0$

$\displaystyle 2x(x-8)+(x-8)$

$\displaystyle (x-8)(2x+1)=0$

$\displaystyle x=8$ or $\displaystyle x=-\frac{1}{2}$

When $\displaystyle x=-\frac{1}{2}$, $\displaystyle y=-32$

$\displaystyle (-\frac{1}{2}, -32)$ are the coordinates of the point where this normal crosses the curve again.