# Thread: Parametric equation.. life application tricky...

1. ## Parametric equation.. life application tricky...

I am having some difficulty understanding this question i would appreciate all the help i can get solving it.

a track on a hill side leading to a house, is in the shape of a smooth curve given parametrically by $x=(3-2t)^2$ $y=(t^3-2t)$

a copy of the hillside is placed in the x-y plane so that a post (P) on the northern end of the track is located at the point where t=2. the hill also follows the equation $x^2+4y^2-4x-12y-12=0$ find

1) the slope of the track at point (P) where the post is located.

2) the equation that can be used to represent the straigh line from the point P to the origin on the x-y plane

3)An expression for the steepness of the hill..

i have though about this but not sure what angle to take this from.. i would really appreciate any help i can get.

2. [QUOTE=sigma1;489557]I am having some difficulty understanding this question i would appreciate all the help i can get solving it.

a track on a hill side leading to a house, is in the shape of a smooth curve given parametrically by $x=(3-2t)^2$ $y=(t^3-2t)$

a copy of the hillside is placed in the x-y plane so that a post (P) on the northern end of the track is located at the point where t=2. the hill also follows the equation $x^2+4y^2-4x-12y-12=0$ find

1) the slope of the track at point (P) where the post is located.[/tex]
the slope is given by $\frac{dy}{dx}= \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$.

2) the equation that can be used to represent the straigh line from the point P to the origin on the x-y plane
Since P is where t= 2, use the parametric equations to find (x, y) at P and then find the equation of the line from (0, 0) to (x, y)

3)An expression for the steepness of the hill..

i have though about this but not sure what angle to take this from.. i would really appreciate any help i can get.
The equation, $f(x,y)x^2+4y^2-4x-12y-12=0$, of the hill is the equation of a circle in the xy-plane which I presume is the outline of the base of the hill. There is no information given about height or steepness. Unless we are to presume that this is a side projection and y is the height. In that case, the steepness of the hill at any point is the length of the gradient of f(x,y) at that point.

3. thanks for the steps. but could you show me how to do the steps you have just outline. this topic is somewat new to me...