## Isabel☺ 2 years ago how will you know if an equation is a parabola, circle, etc.?

1. amistre64

there is a general conic equation; something like x^2 + xy + y^2 + ... that i can never recall if its a standard conic (not twisted at an angle) you can recognize certain proerties

2. amistre64

a parabola only has one square in it a circle will have the same constants for x^2 and y^2, and have a + in the middle an ellipse is like a circle, but it has different constants a hyperbola is like an ellipse, but with a minus sign

3. Isabel☺

uhmm...kay maybe with some examples? oh, wait thanks! :)

4. amistre64

parabola: y = x^2 + .... circle: x^2 + y^2 = 8 ellipse: 4x^2 + 7y^2 = 15 hyperbola: 3x^2 - 2y^2 = 29

5. Isabel☺

so why is y=4-x^2 a parabola?

6. amistre64

generally, becasue it has one sqaured term in it

7. Isabel☺

but (x-h)^2 = 4p (y-k) is the eq. of a parabola right?

8. amistre64

|dw:1359987041116:dw|

9. amistre64

there is an algebra definition and a geometric definition; you presented the geometric one

10. Isabel☺

what's the difference between those definition ?

11. amistre64

one is defined by geometric properties, while te other is defined by arithmetical properties. The two are equivalent, but its just the perspective studies that generated them.

12. amistre64

directrix distance (directrix is a geometric property) v v (x-h)^2 = 4p (y-k) ^ ^ ^ ^ center x center y

13. amistre64

y = 4 -x^2 x^2 = 4 - y (x - 0)^2 = -4/4 (y - 4) p = -1/4; and center (or vertex in this case) is at (0,4)

14. amistre64

cost accting exam starting soon, good luck ;)

15. Isabel☺

thanks! :)