Question

16x2 + 25y2 - 96x - 200y + 144 = 0. Write the standard form of the ellipse.

1) Find the center

2) Find the foci

3) Find the vertices

Answer 1

i'm assuming you know how to complete the square?

Answer 2

yes/no ???

Answer 3

@kenneyfamily I request you to give a proper response to the answerer , give the reply to @dpaInc

Answer 4

no i do not :(

Answer 5

hmm... have you ever heard of the process?
the reason i'm asking is because that is what's needed to put this equation into standard form....

Answer 6

yes i have heard of it

Answer 7

ok... this is our goal.....
\[\huge \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \]
this is standard formm for the equation of an ellipse (one of 'em at least)..
wher (h, k) is the center and "a" and "b" are the lenghts of the major and minor axes , respectively.

Answer 8

so what we need to do first is to group all the x's and all the y's with parenthesis...

Answer 9

\[\large 16x^2 + 25y^2 - 96x - 200y + 144 = 0\]
\[\large (16x^2 - 96x) + (25y^2 - 200y) + 144 = 0\]
\[\large (16x^2 - 96x) + (25y^2 - 200y) = -144\]

still with me here?

Answer 10

before completing the square, we'll need to factor out the 16 and the 25...
\[\large 16(x^2 - 6x) + 25(y^2 - 8y) = -144\]

you ok up to here?

Answer 11

hello?

Answer 12

sorry yes

Answer 13

do you know how to multiply these?:
\(\large (x+1)^2= \)
\(\large (x+5)^2= \)
\(\large (x+7)^2= \)
\(\large (x-1)^2= \)
\(\large (x-5)^2= \)

these will produce "perfect square trinomials." that is what we need in order to "complete the square"

Answer 14

yes

Answer 15

are you able to readily identify whether a trinomial is a perfect square trinomial or not?

Answer 16

yes i believe so

Answer 17

which one are here: