Help please?

Question

What is the graph of 4x^2 + xy + 4y^2 - 8 = 0

Is this an ellipse, hyperbola, a parabola, or a line
How can u tell which 1 of these it is?

Answer 1

You can rule out parabola and line immediately.

line has single power x and y only
parabola has single power y and x² only (or x and y² only)

So it's an ellipse or hyperbola.
An ellipse has the form (x-h)²/a² + (y-k)²/b²=c² [note that if a=b, the ellipse is a circle]
A hyperbola has the form (x-h)²/a² - (y-k)²/b² = c²

My guess therefore is ellipse.

Answer 2

First I warn you to ABSOLUTELY DO NOT MEMORIZE ANY OF THE ABOVE that anyone has written. While it may be correct, memorization in math is like praying to Satan in a Christian church. It is forbidden.

First, look at the equation:
4x^2 + xy + 4y^2 - 8 = 0

Conceptual math would tell you that a line has no powers greater than one in the variables. Thus, a line is eliminated.

A hyperbola's x^2 and y^2 values must be negative. Why? A hyperbola's curves go in opposite directions. Thus, they must be different in terms of their value (positive vs. negative) A hyperbola is eliminated as 4x^2 and 4y^2 are both positive.

A parabola must have a y^2 or x^2 value. NOT BOTH. As a result, a parabola is eliminated.

As a result, only ellipse is left, and it is correct as both x^2 and y^2 terms are positive.

Answer 3

This is actually an ellipse that has been rotated. This is how you can tell. The general equation for a conic section (in two dimensional Cartesian coordinates) is:

Ax^2+Bxy+Cy^2+Dx+Ey+F=0

You need to use the discriminant B^2-4AC (in this case 1^2-4*4*4=-63).
If discriminant < 0, it's an ellipse.
If discriminant = 0, it's a parabola.
If discriminant > 0, it's a hyperbola.

D and E determine horizontal and vertical displacement, respectively, and B determines a rotation (as well as the conic type, as mentioned above). F pretty much determines the size of the thing.

Answer 4

This is an ellipse, since both of the x^2 and y^2

Answer 5

this is equation of the form

ax^2 + by^2 +2gx +2fy + 2hxy + c =0

ok now listen,u just cant look at it and say wht is it ,unless u perform the following tests

first of all calculate this determinant

|a h g |
|h b f | = del
|g f c|

u can remember it as "all hot girls having boy friends go for cinema " lol

now u can test it out very easily
second step is to caluclate h^2 - ab

now ur job is done, look at the table and come to the conclusion

CASE 1

del !=0 (determinant is not equal to zero)
h^2-ab<0 Ellipse
h^2-ab=0 Parabola
h^2-ab>0 Hyperbola


CASE 2
del =0

h^2-ab<0 Point
h^2-ab=0 Pair of parallel or coincident lines, or an imaginary locus
h^2-ab>0 Pair of intersecting lines

CASE 3
if a=b and h=0 the conic is a circle


so now i hope u can selct which one of it is ;)

hope it helps

if u further need any help ,u can im me at escape_velocity009

thanks

Answer 6

this is a circle since a and c, the coeffecients for x and y are equal, or it could be an ellipse since the x and y are both squared.

Answer 7

It is an ellipse.

Lines do not have exponents greater than 1, they can all be expressed as y=mx+b.

A parabola will only have one squared term, not both.