who is super good at alg 2

Question

anteater · Answer

How super good?

anteater · Answer

What sort of question do you have?

anonymous · Answer

alot

anteater · Answer

What is your first question?

anonymous · Answer

hold on its loading

anonymous · Answer

Without writing the equation  in the standard form, state whether the graph of this equation is a parabola, circle, ellipse, or hyperbola. 63x^2-252x+36y^2-72y=-18

anteater · Answer

Do you have an idea on this one? Which conic sections can you rule out immediately?

anonymous · Answer

circle

anteater · Answer

Why did you choose circle?

anonymous · Answer

because it has more then one varible

anteater · Answer

That is one thing to look for, certainly. :) And so you can eliminate parabola.
Why did you eliminate the hyperbola?

anonymous · Answer

idk

anteater · Answer

Hint: look at the signs on the x^2 and y^2 terms.

anteater · Answer

They are both positive. In order for this to be the equation of a hyperbola, what would your equation need to have?

anteater · Answer

The equation of a hyperbola is: (x^2/a^2) - (y^2/b^2) = 1  for a horizontally oriented hyperbola

and (y^2/a^2) - (x^2/b^2) = 1 for a vertically oriented one. 

Now if you took either of these equations and multiplied by a^2 times b^2 to get rid of the fractions, would the sign between the terms change?

anteater · Answer

The signs on the x^2 and y^2 terms would be different. One would be positive and one would be negative. So that is how you can tell if you have a hyperbola. :)

anteater · Answer

So for your equation: 63x^2-252x+36y^2-72y=-18  , the x^2 term is positive and so is the y^2 term. So this can't be a hyperbola. Does that make sense?

anonymous · Answer

yes it does

anteater · Answer

Ok, good. :)  So we are down to a circle and an ellipse.

anteater · Answer

Look at the coefficients on the x^2 and y^2 terms of your equation. What is the coefficient of x^2 and what is the coefficient of y^2?

anteater · Answer

For the term with the x^2 in it, the coefficient is 63. For the term that has a y^2, the coefficient is 36. So ... is this a circle or an ellipse, and why?

anteater · Answer

In order for this to be a circle, what would have to be true of the coefficients of those two terms?

anteater · Answer

The coefficients would have to be the same, in order for this to be a circle, since the major and minor axes would have to be the same length. So in this case, you have an ellipse.

anteater · Answer

So, here is a sort of checklist you could use on this sort of problem. First, make sure to arrange the equation so that all of the terms with variables are on one side of the equation, and the constant term is on the other. Then, look for these features:

1) If there is an x^2 term, but no y^2 term; or if there is a y^2 term, but no x^2 term, you have a parabola.

2) If your equation contains both x^2 and y^2, then check the signs on those two terms. If one is positive and the other negative, then you have the equation of a hyperbola.

3) If the equation is neither that of a parabola or a hyperbola, the next thing you want to do is to look at the coefficients on the x^2 and y^2 terms. If they are the same number, then you have a circle. If not, then you have an ellipse.

I hope this was helpful!

anteater · Answer

If you are still there, please let me know. We can use the checklist to work a similar problem, if you would like.