10.6 General Form

10.6 General Form

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General Form: Ax²+Bxy+Cy²+Dx+Ey+F=0

• 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

Determine the conic section from the general form!

Multiple Choice

$$6x^2+y^2-8x+2y-9=0$$  

• Circle

• Ellipse

• Hyperbola

• Parabola

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

​Ellipse!

Multiple Choice

$$-x^2+7x+y+8=0$$  

• Circle

• Ellipse

• Hyperbola

• Parabola

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

​Parabola!

Multiple Choice

$$9x^2+9y^2-11x+2=0$$  

• Circle

• Ellipse

• Hyperbola

• Parabola

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

​Circle!

Multiple Choice

$$-x^2-6y^2+7x-11y+10=0$$  

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

$$-2x^2+11y^2+2x+2y-3=0$$  

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

$$8x^2-y^2+7x-8y+14=0$$  

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

$$y^2-x+4y+12=0$$  

• Circle

• Ellipse

• Hyperbola

• Parabola

Multiple Choice

$$-4x^2-4y^2+x-9y+12=0$$  

• Circle

• Ellipse

• Hyperbola

• Parabola