Conic Sections

Conics - Discriminant


If AA and BB are nonzero real numbers, what is the condition on AA and BB such that the equation x2A2+y2B2=1 \frac{x^2}{A^2}+\frac{y^2}{B^2} = 1 represents an ellipse that is not a circle?

What is the equation of the line passing through the intersection points of the following two curves: x2+y26x6y+17=0,x2+y210x15y+49=0? {x}^2+{y}^2-6x-6y+17 = 0 , {x}^2+{y}^2-10x-15y+49= 0?

What is the area of the set of points in the bounded region x2+y28x8y+280? {x}^2 + {y}^2 -8x -8y +28 \leq 0 ?

If 5x2+ay2+4x+5y+18=05{x}^2+a{y}^2+4x+5y+18=0 is an equation that represents a circle, what is the value of a?a ?

Which of the following equations represents a different type of conic section than the others?


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