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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 :(
you have to find the equations of the two vertical tangents and the two horizontal tangentsQuote:
Originally Posted by savni98
for the horizontal tangents, y' = 0
for the vertical tangents, y' is undefined.
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 solveQuote:
Originally Posted by savni98
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?
this is incorrectQuote:
Originally Posted by savni98
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?
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.Quote:
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.
Quote:
Originally Posted by savni98
The box is bounded by these four lines! Draw the ellipse, draw the lines, get the box.Quote:
Originally Posted by skeeter