Center
In the center of the conic, the gradient of the quadratic form Q vanishes, so:
We can calculate the center by taking the first two rows of the associated matrix, multiplying each by (x, y, 1)T, setting both inner products equal to 0, and solving the system.
This becomes
Note that in the case of a parabola, defined by (4AC-B2) = 0, there is no center since the above denominators become zero.
Read more about this topic: Matrix Representation Of Conic Sections
Famous quotes containing the word center:
“There is nothing more natural than to consider everything as starting from oneself, chosen as the center of the world; one finds oneself thus capable of condemning the world without even wanting to hear its deceitful chatter.”
—Guy Debord (b. 1931)
“Whenever there’s a big war coming on, you should rope off a big field. And on the big day, you should take all the kings and their cabinets and their generals, put ‘em in the center dressed in their underpants and let them fight it out with clubs. The best country wins.”
—Maxwell Anderson (1888–1959)
“Death is someone you see very clearly with eyes in the center of your heart: eyes that see not by reacting to light, but by reacting to a kind of a chill from within the marrow of your own life.”
—Thomas Merton (1915–1968)