Question

Where is the curve x^2y - xy -x^2 + 10x -12y -21 =0 symmetric?

Answer 1

\[x^2y-xy-x^2-10x-12y-21=0\]

Answer 2

can you get in the form ax^2 + bx + c = 0 ?

Answer 3

erm i couldnt because of the x^2y

Answer 4

-b/2a = (y + 10)/2(y-1)

Answer 5

how did you get that?

Answer 6

@jim_thompson5910 hi would you agree this would be the x-value for the vertex of a parabola or need another approach explicit

Answer 7

i tried to see if i could get it into the general equation of the conic, i couldnt quite get it

Answer 8

This is the graph that I get

https://www.desmos.com/calculator/eguruel3b9

and I don't see any symmetry anywhere. Maybe there's a typo?

Answer 9

I'm thinking that it should be
x^2 - x*y -y^2 + 10x -12y -21 =0
if that's the case, then we get this graph
https://www.desmos.com/calculator/ka8axdps59
which appears to have symmetry

Answer 10

the original has 10x but below you have -10x which is correct?

Answer 11

oh I missed that entirely. Thanks

here is the fixed graph
https://www.desmos.com/calculator/cvfq2jwvjy

Answer 12

@jim_thompson5910 thanks for responding
I see the graph but what is the solution? what would be the equation of the line of symmetry?

Answer 13

Im currently reviewing for my Exit exam and i came across this question, it actually had choices

a) x-axis
b) y-axis
c) origin
d) none at all

Answer 14

I see a line of reflection not of symmetry or would that be the same?

Answer 15

multiple guess I would choose none sorry i could not be of more help

Answer 16

there may be symmetry but I'm not 100% sure. There's definitely no x axis symmetry, no y axis symmetry, and there is no origin symmetry

Answer 17

x axis symmetry happens when you can fold the graph over the x axis to have it line up with itself perfectly

http://www.algebra-online.com/tutorials-4/radical-inequalities/articles_imgs/2199/symmet7.gif

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y axis symmetry happens when you can fold the graph over the y axis to have it line up with itself perfectly

http://mathbitsnotebook.com/Algebra1/FunctionGraphs/symgraph1.gif


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Origin symmetry is where you can rotate a graph 180 degrees around the origin and have it line up with itself perfectly


http://img.sparknotes.com/content/testprep/bookimgs/sat2/math2c/0054/odd.gif

Answer 18

your graph meets none of those criteria so I'd go with `none` as the answer

Answer 19

alright, thanks a lot :D