## ghazi 3 years ago is the equation of ellipse a function?

1. 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.

2. 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?

3. ghazi

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

4. ghazi

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

5. 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)

6. jim_thompson5910

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

7. ghazi

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

8. jim_thompson5910

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

9. jim_thompson5910

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

10. ghazi

well that is one one onto function

11. jim_thompson5910

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

12. ghazi

13. jim_thompson5910

not sure what you mean

14. ghazi

many one onto function?

15. jim_thompson5910

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

16. 08bkrishna

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

17. jim_thompson5910

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

18. 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?

19. jim_thompson5910

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

20. jim_thompson5910

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

21. ghazi

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

22. 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

23. ghazi

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

24. jim_thompson5910

it isn't upright since it's sideways

25. TuringTest

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

26. 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?

27. 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

28. 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...

29. 08bkrishna

@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

30. 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?

31. ghazi

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

32. eliassaab

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

33. ghazi

is it a function or not?

34. eliassaab

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