# Parametric equation.. life application tricky...

• Apr 8th 2010, 07:11 PM
sigma1
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 $\displaystyle x=(3-2t)^2$ $\displaystyle y=(t^3-2t)$

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 $\displaystyle x^2+4y^2-4x-12y-12=0$ 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.
• Apr 9th 2010, 03:27 AM
HallsofIvy
[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 $\displaystyle x=(3-2t)^2$ $\displaystyle y=(t^3-2t)$

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 $\displaystyle x^2+4y^2-4x-12y-12=0$ find

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

Quote:

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)

Quote:

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, $\displaystyle f(x,y)x^2+4y^2-4x-12y-12=0$, 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.
• Apr 9th 2010, 04:20 AM
sigma1
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...