Question

find the equations of the tangent lines to 9x^2 + 16y^2 = 52 that are parallel to the line 9x-8y =1

Answer 1

define your dy/dx

Answer 2

81/128

Answer 3

slope = 9/16

Answer 4

correction ! slope = 81/128

Answer 5

9x^2 + 16y^2 = 52

9x + 16y y' = 0

y' = -9x/16y

Answer 6

for this to be parallel to the given line; we want it to equal:

9x-8y =1

9-8y' =0

y' = 9/8

Answer 7

since slope = y/x meaning that the points are (8 , 9)?

Answer 8

\[\frac{9x}{16y}=-\frac{9}{8}\]solve for x,y

Answer 9

we have to equate the derivatives to determine the (x,y) points

Answer 10

ohhhh... okay okay

Answer 11

i misplaced a negative, but i think it amounts to the same thing :)

Answer 12

72x = 144y

Answer 13

x = 2?

Answer 14

\[-\frac{9x}{16y}=\frac{9}{8}\]
\[-\frac{9x}{1}=\frac{9~2y}{1}\]
\[-x=2y~:~y=-\frac12x\]

Answer 15

no x = 2y

Answer 16

oops! i forgot y XD

Answer 17

and actually its x = -2y , I think ..

Answer 18

Or we can just look at the great work that @amistre64 has done.

Answer 19

9x^2 + 16y^2 = 52; x=-2y is fine too

94y^2 + 16y^2 = 52

Answer 20

yes. negative sign too since it was misplaced hahaha

Answer 21

solving for the x,y is just a matter of plugging in ....
then you can apply the slope to those points

Answer 22

that not 94y^2, its 9*4y^2 :)

Answer 23

y = 1?

Answer 24

y = 1 or -1 yes

Answer 25

since y = 1
x = 2y
x = -2(1)
x = -2

Answer 26

good, x = 2 or -2 i believe

Answer 27

you have 4 points, and can prolly narrow it down to the correct 2 since the original i believe is an ellipse

Answer 28

9x + 8y =-26

Answer 29

Actually you only have 2 points. It can only be y = -1 or 1.

When y = -1 x = 2 and when y = 1 x = -2 so the two points are (-2, 1) and (2,-1)

Answer 30

http://www.wolframalpha.com/input/?i=9x%5E2+%2B+16y%5E2+%3D+52%2C+y%3D9%28x-2%29%2F8-1%2C+y%3D9%28x%2B2%29%2F8%2B1%2C+9x-8y%3D1

Answer 31

(-2,1) and (2,-1) are lovely

Answer 32

wow. that is a really neat graph!

Answer 33

it took me weeks to make it lol

Answer 34

Sweet wolfram curve @amistre64 . I need to become more adept at using that site.

Answer 35

lol yeeeeaaaaahhh

Answer 36

thank you for all of your efforts. both of you!

Answer 37

Credit goes to @amistre64 he/she carried the majority of the work load!

Answer 38

I just made comments from the cheap seats.

Answer 39

its hard to seperate the extra chatter from the voices in my head :)