is the equation of ellipse a function?

- ghazi

is the equation of ellipse a function?

- katieb

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- jim_thompson5910

No it is not. You can pass a vertical line through it and it will pass through more than one point. So it fails the vertical line test.

- ghazi

okay ...what if i write it as function of y ..i mean just consider standard equation of ellipse and separate both the variables..like y in terms of x....so can't we call it function?

- ghazi

y=bsqrt (1-x^2/a)

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## More answers

- ghazi

\[y=b * \sqrt (1-x^2/a)\]

- jim_thompson5910

Circle (special type of ellipse)
x^2 + y^2 = r^2
y^2 = r^2 - x^2
y = +-sqrt(r^2 - x^2)
y = sqrt(r^2 - x^2) or y = -sqrt(r^2 - x^2)

- jim_thompson5910

The last line gives it away that it can't be a function

- ghazi

okay...by the way what is the accurate and precised definition of function?

- jim_thompson5910

A function is something that maps each input to EXACTLY ONE output

- jim_thompson5910

With ellipses and circles, inputs map to more than one output

- ghazi

well that is one one onto function

- jim_thompson5910

no, a one to one function is each input is mapped to one unique output

- ghazi

and what about many one?

- jim_thompson5910

not sure what you mean

- ghazi

many one onto function?

- jim_thompson5910

if you mean multiple inputs lead to the same output, then that's still a function

- anonymous

if you mean a manyt-to-one function, that is a proper function. a basic example would be x^2, where, e.g. -2 and 2 map to 4

- jim_thompson5910

it's a function if you only get one output per input

- ghazi

yes that's what i mean and @jim_thompson5910 if i pass a vertical line through a parabola still it cuts parabola at two points |dw:1345840885553:dw| isn't it a fucntion ...the equation of parabola?

- jim_thompson5910

that's not a function since it fails the vertical line test

- jim_thompson5910

that's the equation x = y^2 or something similar to that

- ghazi

@jim_thompson5910 it could be a function if it gives you two output by one input as @08bkrishna said

- jim_thompson5910

btw, the parabola has to be upright to be a function
Just because it's a parabola, it doesn't automatically make it a function

- ghazi

well x=y^2 is a parabola....no need to be upright

- jim_thompson5910

it isn't upright since it's sideways

- TuringTest

in your example x is a function of y, but not vice versa

- ghazi

@eliassaab can you help with this...please ..and @jim_thompson5910 i said why do i need it to be upright? for considering it parabola?

- jim_thompson5910

yes that terminology is correct TuringTest...but confusing because x is usually the input, which means that x=y^2 isn't a function

- ghazi

well jim ...i have to check this out...especially your definition of function....cuz i know there is many one into function in which one input leads to many output...

- anonymous

@ghazi, a many to one function is where more that one input leads to the same output. this is different to a one to many, where one input leads to multiple outputs. the former is considered an equation, while the latter isn't

- jim_thompson5910

The whole point of the function is to predict the output. But if you get more than one output, then which output will you choose?
Ex: If I have a "function" of the price of a car (y) after some number of years (x), then which price will I choose if I get more than one outputs for a particular x value?

- ghazi

yea agreed...thank you...it was a big confusion....special thanks to @jim_thompson5910 , @08bkrishna

- anonymous

\[
\frac {x^2} {a^2}+\frac {y^2} {b^2}=1
\]

- ghazi

is it a function or not?

- anonymous

For each value of x, except x=a or x=-a, y has two values. So it is not a function.

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