1. ## Calc help asap

The graph of an ellipse is x^2-xy+y^2 = 3 is shown. What are the dimensions and the location of the box containing the ellipse.

note: the sides of the box are vertical and horizontal and also are tangent to the ellipse.

I NEED HELP. I went about to find the derivative first but I honestly have no idea on where to go from here on.. please help

2. Originally Posted by savni98
The graph of an ellipse is x^2-xy+y^2 is shown. What are the dimensions and the location of the box containing the ellipse.

note: the sides of the box are vertical and horizontal and also are tangent to the ellipse.

I NEED HELP. I went about to find the derivative first but I honestly have no idea on where to go from here on.. please help
you have to find the equations of the two vertical tangents and the two horizontal tangents

for the horizontal tangents, y' = 0

for the vertical tangents, y' is undefined.

3. hey, i did that and I got for the y'=0..y=2x and for the y'=undefined i got y=-x/2

4. Originally Posted by savni98
hey, i did that and I got for the y'=0..y=2x and for the y'=undefined i got y=-x/2
sub those back into the original curve equation and solve

5. yeah, i did that too and im getting weird values like x^2=3 so x=+-sqrt3 and y^2=1 so y=+-1 for the y'=0. and i get x^2=3/5 so x=+-sqrt3/5 and y^2=3/10 so y=+-sqrt3/10 for the y'=undefined. do those seem reasonable?

6. Originally Posted by savni98
hey, i did that and I got for the y'=0..y=2x and for the y'=undefined i got y=-x/2
this is incorrect

7. nvm i corrected myself and for the first part y'=0 i got x=+-1 and y=+-2. but for the y'=undefined, im kinda confused, don't you just set the bottom of the derivative to 0?

8. heyy sorry now i got all 4 points, but from there how do i find the actual location of the box and the dimensions??

9. Originally Posted by savni98
heyy sorry now i got all 4 points, but from there how do i find the actual location of the box and the dimensions??
Draw a box around the ellipse and label the points you have found. Now use simple geometry to get the dimensions of the box.

10. well since the ellipse is tilted and therefore not symetrically to the x and y axis, the points i found are not the vertices of the box and i think when i drew it out, the points i got were actually tangent to the box. how do i go about finding the actual vertices.

11. Originally Posted by savni98
well since the ellipse is tilted and therefore not symetrically to the x and y axis, the points i found are not the vertices of the box and i think when i drew it out, the points i got were actually tangent to the box. how do i go about finding the actual vertices.
Originally Posted by skeeter
you have to find the equations of the two vertical tangents and the two horizontal tangents
[snip]
The box is bounded by these four lines! Draw the ellipse, draw the lines, get the box.