<Dd> A x 2 + B x y + C y 2 + D x z + E y z + F z 2 = 0 . (\ displaystyle Ax ^ (2) + Bxy + Cy ^ (2) + Dxz + Eyz + Fz ^ (2) = 0 .) </Dd> <P> Or in matrix notation </P> <Dl> <Dd> (x y z) (A B / 2 D / 2 B / 2 C E / 2 D / 2 E / 2 F) (x y z) = 0 . (\ displaystyle \ left ((\ begin (matrix) x&y&z \ end (matrix)) \ right) \ left ((\ begin (matrix) A&B / 2&D / 2 \ \ B / 2&C&E / 2 \ \ D / 2&E / 2&F \ end (matrix)) \ right) \ left ((\ begin (matrix) x \ \ y \ \ z \ end (matrix)) \ right) = 0 .) </Dd> </Dl> <Dd> (x y z) (A B / 2 D / 2 B / 2 C E / 2 D / 2 E / 2 F) (x y z) = 0 . (\ displaystyle \ left ((\ begin (matrix) x&y&z \ end (matrix)) \ right) \ left ((\ begin (matrix) A&B / 2&D / 2 \ \ B / 2&C&E / 2 \ \ D / 2&E / 2&F \ end (matrix)) \ right) \ left ((\ begin (matrix) x \ \ y \ \ z \ end (matrix)) \ right) = 0 .) </Dd>

The cartesian coordinate system can be applied to three dimensional solids instead of two axes