Graphing Symmetry Question II?

Question

X^2 - 2X - Y^2=4
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(1)^2 - 2(1) -y^2=4,,
1 - 2 -y^2 = 4,,
(-1) - y^2 = 4,,
-y^2 = 5,,
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(-1)^2 - 2(-1) -y^2=4,,
1 +2 - y^2 =4..
3 - y^2 = 4..
-y^2 = 1..
y^2 = (-1)..
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I know this exhibits x-axis, and y-axis symmetry. however, I believe it is not because I have obtained an equivent equation by replacing a postive value with a negative. I believe it is because of obtaining the irrational solution. Is this correct to think along these lines? Am I choosing incorrect values maybe, to test for symmetry?
Thank you kindly " once again."

Answer 1

For a graph, go to www.quickmath.com, click on Plot under Equations, and type in

x^2 - 2x - y^2 = 4

Just like that

Set the margins as big or small as you need them to be, and click plot.

Also make sure that the letters are lowercased.

Answer 2

X^2 - 2X - Y^2=4 it is not symmetrical approximately x axis, by way of fact it extremely is shape is that of a a million/2 circle by way of fact Y won't be able to be detrimental (Y = (4-x^2+2*x)^0.5) they gotta to be effective authentic numbers. and yea it extremely is symmetrical approximately some vertical line: x=2.2361. I have been given this from a graphing utility yet. =============================== authentic!! I forgot to putt detrimental examine in front of that y=.. >< oops! sorry. I lost marks for this mistake like 2 years in the past in a try, yet I made that mistake back anyhow try graphing it, it extremely is the superb way!

Answer 3

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oooooooohhhhhhh!! SORRY !!hhhhhooooooooooo EDITED!
Thus (x-1)^2 –1 –y^2 =4; (y(x))^2 = (x-1)^2 -5;
■ (y(-x))^2 = (x+1)^2-5, thence y^2 is not symmetrical w.r.t. y-axis, so y(x) is also not symmetrical w.r.t. y-axis;
■ (-y(-x))^2 = (y(-x))^2 = (x+1)^2 -5 =/= (y(x))^2 = (x-1)^2 -5;
■ (-y(x))^2 = (y(x))^2 is symmetrical w.r.t. x-axis!
thus no symmetry w.r.t. the origin.
▒ but y(x) is symmetrical w.r.t. vertical axis x=1;
▒ but y(x) is symmetrical w.r.t. point (1,0);
☺ so graph function y(t) = +sqrt(t^2-5) for t>sqrt5; then mirror it w.r.t. y-axis; then mirror all w.r.t. x-axis; then transfer y-axis 1 unit to the left; this will be y(x).