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Chapter 10: Q 7. (page 676)

Except for degenerate cases, the equationAx2+Bxy+Cy2+Dx+Ey+F=0defines an ellipse if ________ .

Short Answer

Expert verified

Except for degenerate cases, the equationAx2+Bxy+Cy2+Dx+Ey+F=0defines an ellipse ifB2-4AC<0.

Step by step solution

01

Step 1. Given information

An equation isAx2+Bxy+Cy2+Dx+Ey+F=0

02

Step 2. Fill in the blank.

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

IfB2-4AC<0, an equation defines an ellipse ifB2-4AC<0

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