10.6 General Form

• Circle: A=C, so both coefficients on the squared variables are the exact same

• Parabola: A or C is zero, so only one variable is squared

• Ellipse: A and C have the same sign (AC>0)

  So the coefficients on squared variables are different numbers, but are either both positive or both negative

• Hyperbola: A and C have different signs (AC<0) So the coefficients on squared variables are different numbers, and have opposite signs

6x²+y²-8x+2y-9=0​ is an ellipse because the coefficients on x² and y² are different numbers, and both positive!

​Ellipse!

-x²+7x+y+8=0 is a parabola because there is only one variable that is squared.

​Parabola!

9x² + 9y²-11x+2=0​ is a circle because the coefficients on x² and y² are the same numbers!

​Circle!