Question

Find the points at which the graph of the equation has a vertical or horizontal tangent line.
4x2 + 16y2 – 72x – 96y + 404 = 0
horizontal tangents (x, y) =
vertical tangents (x, y) =

Answer 1

and satellite i wnated to thankyou again but my comp froze..lol..please help me on this one as well:)

Answer 2

sattelite can you please help me out on this one...

Answer 3

sure

Answer 4

oh man another implicit diff? hold on i will write it out on paper

Answer 5

Find the points at which the graph of the equation has a vertical or horizontal tangent line. (Order your answers from smallest to largest x, then from smallest to largest y.)
4x2 + 16y2 – 72x – 96y + 404 = 0
horizontal tangents (x, y) = ( ), ( )
vertical tangents (x, y) = ( ), ( )

Answer 6

oki cool...thankyou so much for this thought...a guy by the name of bahrom recomended you:)

Answer 7

yeah i got it.

Answer 8

horizontal tangent when x = 9

Answer 9

vertical when y = 3

Answer 10

put in x = 9 to find the corresponding y and vice versa

Answer 11

leme try

Answer 12

try the x i will try the y = 3

Answer 13

k..im confused about where and how to plug it in

Answer 14

i got x = 9 you need y. replace x by 9 in original equation to find y

Answer 15

oki

Answer 16

ugh im confused i know what you saying but im screwing up the algebra:(

Answer 17

damn i get no answer. let me try again

Answer 18

oki

Answer 19

ok i got this
\[y'=\frac{8x-72}{96-32y}\] and i am fairly certain this one is right

Answer 20

because i did it twice. horizontal tangent means numerator = 0 so i set
\[8x-72=0\]
get
\[x=9\]

Answer 21

the problem is when i replace x by 9 in original equation and solve for y i get no solution

Answer 22

wait but its asking for points

Answer 23

ok here is the answer

Answer 24

so what would the pooint sets be:S

Answer 25

horizontal, x = 9, y = 1

Answer 26

vertical x = 5, y = 3

Answer 27

oh wait. there are two for each

Answer 28

its saying thats inccorect

Answer 29

maybe theres 4 sets of points

Answer 30

so here is final answer:
horizontal
x=9, y = 1
x = 9, y = 5
vertical
x = 5, y = 3
x = 13, y = 3

Answer 31

it is an ellipse so two vertical and two horizontal ones algebra is a pain pain pain

Answer 32

:)...yes omg thankyou

Answer 33

please don't tell me that was wrong

Answer 34

oh whew

Answer 35

no it was right lol hence im saying thanks

Answer 36

do u mind helkping me on anything els..i have a few from another section too

Answer 37

i have about another 15 minutes in me