Asked by Emily
"Sketch the ellipse. Find the coordinates of its vertices and foci.
34. x^2 + 25y^2 - 6x - 100y + 84 = 0
(Hint: Complete the squares in x and y. Begin by writing the equation in this form: (x^2 - 6x + ___) + 25(y^2 - 4y + ___) = -84.)"
==> I used the hint that came with the problem, but as I tried to solve the equation into the general form for an ellipse, I was getting negative denominators, which would make a and b contain imaginary numbers. Does anyone know how to solve this? Any help is greatly appreciated! :)
34. x^2 + 25y^2 - 6x - 100y + 84 = 0
(Hint: Complete the squares in x and y. Begin by writing the equation in this form: (x^2 - 6x + ___) + 25(y^2 - 4y + ___) = -84.)"
==> I used the hint that came with the problem, but as I tried to solve the equation into the general form for an ellipse, I was getting negative denominators, which would make a and b contain imaginary numbers. Does anyone know how to solve this? Any help is greatly appreciated! :)
Answers
Answered by
Reiny
x^2 + 25y^2 - 6x - 100y + 84 = 0
x^ - 6x + 9 + 25(y^2 - 4y + 4) = -84 + 9 + 100
notice in the y expression, I added 4 to the inside, but that was multiplied by 25, so I had to add 100 on the right side.
(x-3)^2 + 25(y-2)^2 = 25
(x-3)^2/25 + (y-2)^2 = 1
so a^2 = 25, and b^2 = 1
take it from there
x^ - 6x + 9 + 25(y^2 - 4y + 4) = -84 + 9 + 100
notice in the y expression, I added 4 to the inside, but that was multiplied by 25, so I had to add 100 on the right side.
(x-3)^2 + 25(y-2)^2 = 25
(x-3)^2/25 + (y-2)^2 = 1
so a^2 = 25, and b^2 = 1
take it from there
Answered by
Emily
Ohhhhh!!!!! This totally makes sense. I forgot to multiply the 4 by 25 before bringing it over to the other side. Thanks so much!! :D
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.