Chapter 10: Q. 9 (page 700)

Identify each conic without completing the square or rotating axes. $x^{2} - 6 x y + 9 y^{2} + 2 x - 3 y - 2 = 0$

Short Answer

Expert verified

The answer is Parabola.

Step by step solution

Step 1. Given information

The given equation of conic is $x^{2} - 6 x y + 9 y^{2} + 2 x - 3 y - 2 = 0$

Step 2. Identify the conic without completing the square or rotating axes.

If the equation is in the form of $A x^{2} + B x y + C y^{2} + D x + E y + F = 0$

Defines,

role="math" localid="1647880928143" $B^{2} - 4 A C = 0, P a r a b o l a B^{2} - 4 A C > 0, E l l i p s e B^{2} - 4 A C < 0, H y p e r b o l a$

On comparing the given equation with the above equation

$A = 1; B = - 6; C = 9; D = 2; E = - 3; F = - 2$

Step 3. Verification of conditions

Let us verify for the conic

$\begin{array}{rcl} B^{2} - 4 A C & = & {(- 6)}^{2} - 4 (1) (9) \\ = & 36 - 36 \\ = & 0 \end{array}$

Therefore, the given conic is Parabola.

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Identify each conic without completing the square or rotating axes. $x^{2} - 6 x y + 9 y^{2} + 2 x - 3 y - 2 = 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify the conic without completing the square or rotating axes.

Step 3. Verification of conditions

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Identify each conic without completing the square or rotating axes.x2-6xy+9y2+2x-3y-2=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Identify the conic without completing the square or rotating axes.

Step 3. Verification of conditions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

Identify each conic without completing the square or rotating axes. $x^{2} - 6 x y + 9 y^{2} + 2 x - 3 y - 2 = 0$