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Conic Sections

Parabolas, ellipses, and hyperbolas, oh my! Learn about this eccentric bunch of shapes.

Discriminant of a Conic

If \(A\) and \(B\) are nonzero real numbers, what is the condition on \(A\) and \(B\) such that the equation \[ \frac{x^2}{A^2}+\frac{y^2}{B^2} = 1\] 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: \[ {x}^2+{y}^2-6x-6y+17 = 0 , {x}^2+{y}^2-10x-15y+49= 0?\]

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

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

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

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