Chapter 10: Q 7. (page 676)

Except for degenerate cases, the equation $A x^{2} + B x y + C y^{2} + D x + E y + F = 0$ defines an ellipse if ________ .

Short Answer

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Except for degenerate cases, the equation $A x^{2} + B x y + C y^{2} + D x + E y + F = 0$ defines an ellipse if $B^{2} - 4 A C < 0$ .

Step by step solution

Step 1. Given information

An equation is $A x^{2} + B x y + C y^{2} + D x + E y + F = 0$

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.

If $B^{2} - 4 A C < 0$ , an equation defines an ellipse if $B^{2} - 4 A C < 0$

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Except for degenerate cases, the equation $A x^{2} + B x y + C y^{2} + D x + E y + F = 0$ defines an ellipse if ________ .

Short Answer

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Step 1. Given information

Step 2. Fill in the blank.

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Fill in the blank.

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Most popular questions from this chapter

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Logic and Functions

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Except for degenerate cases, the equation $A x^{2} + B x y + C y^{2} + D x + E y + F = 0$ defines an ellipse if ________ .