conics confusion (1 Viewer)

[ianc]

Hey there, just have a simple question:

With the formula for the ellipse and hyperbola, are a and b always the numbers under x^2 and y^2 respectively? (i get confused about which numbers to plug in to the formulas such as b^2=a^2(e^2-1)

eg with the ellipse x^2/9 + y^2/4; does a=3 and b=2 or vice versa?

Thanks!

 

[davin]

for an ellipse, the numbers under x^2 and Y^2 are used to indicate which direction the ellipse opens. in other words, whichever one is bigger is a, because the larger axis is the major axis. so a=3 in X^2/9 + y^2/4=1 or in x^2/4 + y^2/9=1 because for both of those, the larger axis is always a.

for a hyperbola, it has a similar purpose, but in this case, a is always the first denominator and b is always the second denominator, and the order of x and y change.
so, for example, a=3 in both x^2/9 - y^2/4 =1 and y^2/9 - x^2/4 = 1


hopfully that covers what you're asking

 

[ianc]

thanks for that. got an exam tomorrow, but conics haven't gotten any easier since i last tried them

 

[_ShiFTy_]

I also prefer Davin's method. Your school might let 'a' and 'b' be something else

When it comes to ellipses, your 'a' is always the bigger number
When it comes to hyperbolas, your 'a' is always the first number

This ensures the formula you use will always stay the same
b^2=a^2(e^2-1)
b^2=a^2(1-e^2)

 

[YBK]

we let a be the x-intercept, and b the y-intercept.

 

[DraconisV]

And with the B to A conversion formulas;

- for the ellipses just think E for Ellipse, so the E comes first, b^2=a^2(e^2-1)

- And the e is last in hyperbola, cause well its the other one, b^2=a^2(1-e^2)

I got confused badly with those before. Umtil i though up the e for ellipse.

Im just so happy that the conics topic is done for now. Woah it was a massive and patience testing topic, ahh.
Yippie onto polynomials, yea 2 lessons and that topic will be done, boo yaa.

Well I hope I helped mate.

 

[pLuvia]

Actually you're wrong.
For ellipse b²=a²(1-e²)
For hyperbola b²=a²(e²-1)

 

[onebytwo]

nice one pluvia

 

[DraconisV]

Actually the e is last in ellipse coz it ends with an E, so ha

(Nice Save)

To much conics makes me confused with the basics