Chapter 10: Q 9. (page 676)

True or False
The equation $3 x^{2} + B x y + 12 y^{2} = 10$ defines a parabola if $B = - 12$ .

Short Answer

Expert verified

The statement is true.

Step by step solution

Step 1. Given information

An equation is $3 x^{2} + B x y + 12 y^{2} = 10$ .

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

Put $B = - 12$ in the equation, $3 x^{2} + B x y + 12 y^{2} = 10$ .

$3 x^{2} - 12 x y + 12 y^{2} = 10$

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

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

Here,

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

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

$\begin{array}{rcl} B^{2} - 4 A C & = & 0 \\ (- 12)^{2} - 4 \times 3 \times 12 & = & 144 - 144 \\ = & 0 \end{array}$

which is true.

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

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True or False
The equation $3 x^{2} + B x y + 12 y^{2} = 10$ defines a parabola if $B = - 12$ .

Short Answer

Step by step solution

Step 1. Given information

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

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True or FalseThe equation 3x2+Bxy+12y2=10defines a parabola ifB=-12.

Short Answer

Step by step solution

Step 1. Given information

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Probability and Statistics

Logic and Functions

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

True or False
The equation $3 x^{2} + B x y + 12 y^{2} = 10$ defines a parabola if $B = - 12$ .