anonymous
  • anonymous
I need some help with this question on conics: Find an equation for the ellipse with the foci (1,1) and (-1,-1) and a major axes of length 4.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
This is a shifted conic, i need to find the equation of this shifted conic
dumbcow
  • dumbcow
this looks like an ellipse with a slanted major axis, is that correct?
anonymous
  • anonymous
yes thats correct

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
It lies on the rotated XY coordinate axes
dumbcow
  • dumbcow
ok the axis is the line y=x, since it goes grough both foci points 2a = 4 a = 2 imagine a triangle with equal legs and hypotenuse of 2 x =y = 2/sqrt2 = sqrt2 verticis are (sqrt2, sqrt2), (-sqrt2, -sqrt2)
dumbcow
  • dumbcow
minor axis must be perpendicular so on the line y=-x length of minor axis is 2b, c is length of foci point from origin --> c=sqrt2 a^2 = b^2 +c^2 2^2 = b^2 +(sqrt2)^2 4 = b^2 +2 b = sqrt2 again imagine 45-45 -90 triangle with hypotenuse of sqrt2 x=y=1 minor verticis = (-1,1) (1,-1)
anonymous
  • anonymous
Shoudlnt we incorporate those formulas x=Xcos(theta)-Ysin(theta) and y=Xsin(theta)+Ycos(theta)
anonymous
  • anonymous
because i am looking for the equation of the rotated ellipse
dumbcow
  • dumbcow
yes to get the equation we have to rotate 45 degrees to get major axis on line y=x now we have a,b so equation of non-rotated ellipse is: \[\frac{x^{2}}{4}+\frac{y^{2}}{2} = 1\] theta = 45 sin(45) = cos(45) = sqrt2/2 \[x' = \sqrt{2}/2(x-y)\] \[y' = \sqrt{2}/2 (x+y)\] replace x with x' and y with y' in equation
anonymous
  • anonymous
Okay i got the equation of the non rotated ellipse, but now i understand how to get the equation of the rotated ellipse. Thank you.
anonymous
  • anonymous
if you could take a look at my other question regarding a helix and curvature, it would be much appreaciated
dumbcow
  • dumbcow
ok

Looking for something else?

Not the answer you are looking for? Search for more explanations.