contour diagram

[rocketrawr]

Let the function f : R^2 ---> R be given by
f(x; y) = x^2 - 2x - 4y^2 - 16y - 15
Sketch the contour diagram of f by drawing the contours f = -2, -1, 0, 1, 2


please help i graphed the contour diagram but i am struggling to solve for each values of f listed above...i think im messing soemthing up when i try to the complete the square of the function.
can anyone show me what to do for a couple of the f values please?

 

[Deleted member 4993]

Let the function f : R^2 ---> R be given by
f(x; y) = x^2 - 2x - 4y^2 - 16y - 15
Sketch the contour diagram of f by drawing the contours f = -2, -1, 0, 1, 2


please help i graphed the contour diagram but i am struggling to solve for each values of f listed above...i think im messing soemthing up when i try to the complete the square of the function.
can anyone show me what to do for a couple of the f values please?

f = (x-1)[sup:24mxsycw]2[/sup:24mxsycw] - (2y + 4)[sup:24mxsycw]2[/sup:24mxsycw]

So your contour maps will be hyperbolas

For f = 2

2 = (x-1)[sup:24mxsycw]2[/sup:24mxsycw] - 4(y + 2)[sup:24mxsycw]2[/sup:24mxsycw]

The equation of the hyperbola would be:

\(\displaystyle \frac{(x-1)^2}{(\sqrt{2})^2} \ - \ \frac{(y+2)^2}{({\frac{1}{\sqrt{2}}})^2} \ = \ 1\)

Now plot the hyperbola - and continue.....