Hey guys, just ran across this question on a homework:
"Find the center of the conic section whose equation is: A x ²+B xy +C y ²+D x +E y +F=0"
How do I find them without any numbers in each term? Is there a general formula to solve for the center like -b/2a?
Any help is appreciated
If B = 0 then it's fairly easy. As Mathstud28 suggested you can complete the square on the x and/or y terms (as applicable) and simplify from there. If B is not 0 then you need to rotate the coordinate system such that the new form has the x'y' coefficient equal to 0.
The question is odd. There is no way to approach this until at least some of the coefficients are known.
That is exactly word for word what the question says. The center (because of the fact that the graph is NOT a parabola since both x and y are both squared) should be that of an eclipse. But I still don't know how to solve for it!!! Does the problem want me to plug numbers in?
If you haven't been taught about Rotations,
. . this problem is inappropriate.
There is a "discriminant": .Find the center of the conic section whose equation is:
. . .
If there is no -term , it is a standard conic.
. . Its axes are parallel to the coordinate axes.
If , the conic has been rotated through angle
. . where: .
We can "un-rotate" the graph with these conversions:
We also have:
We get a new equation: .
. . and now you can complete the square, etc.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Note: They always use the term "center".
. . . . .In a parabola, it refers to the vertex.