How would you turn this equation for an ellipse 2(x+4)^2 + 3(y-1)^2 = 24 into standard form??

Question

tkhunny · Answer

Which Standard form is that?

Perhaps multiply out the squares, collect like terms, and you will be close?

jellybot23 · Answer

Well isn't standard form (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1?

jellybot23 · Answer

@tkhunny

tkhunny · Answer

Yes, that is a standard form for an ellipse.  That's why I asked.  Just divide by 24 to get that standard form,

There is also the standard quadratic form:  $ax^{2} + bxy + cy^{2} + dx + ey + f = 0$

In our case, b = 0, but everything else might be there.

jellybot23 · Answer

Would I have to simplify because there is a 2 in front of (x+4) and a 3 in front of (y-1)? @tkhunny

tkhunny · Answer

Just divide by 24.  $\dfrac{2x^{2}}{24} = \dfrac{x^{2}}{12}$

jellybot23 · Answer

Okay that's what I thought, but I wanted to make sure! I haven't dealt with ellipse equations yet this year where the bottom number wasn't a Perfect square, so I was a little disoriented haha
Thank you!

tkhunny · Answer

Next time, SHOW what you thought.  It makes for more pleasant conversation.  :-)