Asked by Joe
Consider the ellipse plotted by x^2+9y^2=9. Find the y-coordinate of the point on the ellipse that is farthest from the point (0,1).
Your answer should be expressed as a fraction of whole numbers.
Your answer should be expressed as a fraction of whole numbers.
Answers
Answered by
Steve
Let the point be (h,k)
The distance d is thus
d^2 = x^2 + (y-1)^2
but, we know that x^2 = 9 - 9y^2, so
d^2 = 9-9y^2 + (y^2-2y+1)
= 10 - 2y - 8y^2
dd/dy = -2 - 16y = -2(1+8y)
so, y = -1/8
and you can get x
The distance d is thus
d^2 = x^2 + (y-1)^2
but, we know that x^2 = 9 - 9y^2, so
d^2 = 9-9y^2 + (y^2-2y+1)
= 10 - 2y - 8y^2
dd/dy = -2 - 16y = -2(1+8y)
so, y = -1/8
and you can get x
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.