Can you help me find the length of the minor and major axis of this elipse
\frac{(x - 1)^2}{12} + \frac{(y + 4)^2}{24}=1

Question

Can you help me find the length of the minor and major axis of this elipse
\frac{(x - 1)^2}{12} + \frac{(y + 4)^2}{24}=1

anonymous · Answer

what you know

tkhunny · Answer

Enclose your LaTeX in \ ( and \ ) (without spaces)

$\dfrac{(x - 1)^2}{12} + \dfrac{(y + 4)^2}{24}=1$

Generally, "dfrac" gives better results than "frac".

mathmale · Answer

$$\frac{(x - 1)^2}{12} + \frac{(y + 4)^2}{24}=1$$   Hint:  You can get the lengths of the major and minor axes from the denominators 12 and 24.

Which one is larger?  This info will tell you whether your ellipse is vertical or horizontal.  Which do you think it is?  Vertical or horizontal?

anonymous · Answer

vertical i don't know why though can you tell me how to find that?

anonymous · Answer

24 is bigger so it is in the major axis but is it just 24 or is there another step?

anonymous · Answer

@mathmale

tkhunny · Answer

It's only about size in an ellipse.  24 > 12, so the major axis is vertical.

If $b^{2} = 12\;then\;2b = ??$  The length of the Minor Axis.

mathmale · Answer

24 is obviously larger than 12.  Since that 24 is underneath the (y+4)^2 term, your ellipse is a VERTICAL one, and your major axis, ' a ', has the length Sqrt(24).  

Please try simplifying Sqrt(24), as well as Sqrt(12).

a = length of major axis:  Sqrt(24)
b = length of minor axis:  Sqrt(12).

anonymous · Answer

a=4.9 b=3.46

anonymous · Answer

is this right? @mathmale

anonymous · Answer

@tkhunny

tkhunny · Answer

Is 3.46 the square root of 12?  Show a little confidence.

anonymous · Answer

yeah

mathmale · Answer

@erob:  tkhunny was correct:  the length of the whole major axis is 2a.

Regarding finding the square roots of 12 and 24:  Here's what I'd suggest:

$$\sqrt{12}=\sqrt{4*3}=\sqrt{4}\sqrt{3}=2\sqrt{3}$$  It's true that this boils down to about 3.46, but 2Sqrt(3) is more elegant and has no round-off error.