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Chapter 10: Q 9. (page 676)

True or False

The equation 3x2+Bxy+12y2=10defines a parabola ifB=-12.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Step 1. Given information

An equation is3x2+Bxy+12y2=10.

02

Step 2. State whether the statement is true or false.

Put B=-12in the equation, 3x2+Bxy+12y2=10.

3x2-12xy+12y2=10

Compare this equation with the general equation of a polynomial, containing two variables,

Ax2+Bxy+Cy2+Dx+Ey+F=0,

Here,

A=3,B=-12,C=12

Now as any second degree polynomial, containing two variables, represents a parabola, if

B2-4AC=0(-12)2-4脳3脳12=144-144=0

which is true.

So, the given equation represents a parabola, which is a true statement.

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Most popular questions from this chapter

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

Semi elliptical Arch Bridge An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20meters wide. The center of the arch is 6meters above the center of the river. See the figure. Write an equation for the ellipse in which the x-axis coincides with the water level and the y-axis passes through the center of the arch.

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