Chapter 9.3, Problem 96E

To determine

To match the equation with the given graphs.

Answer to Problem 96E

• 1(b)
• 2(a)
• 3(d)
• 4(c)

Explanation of Solution

Given Data:

Figures:

1.

  

2.

  

3.

  

4.

  

Given equation is $4x^2-y^2-8x-2y-13=0$ .

Calculation:

Compare the equation with

  $\begin{array}{l}A{x}^2+C{y}^2+Dx+Ey+F=0\\ A=4,C=-1,D=-8,E=-2,F=-13\\ \mathrm{Here}AC=-4<0\end{array}$

So equation represents a hyperbola .

Hence the matching graph is $1(b)$ .

Given equation is $x^2+y^2-2x-8=0$

  $\begin{array}{l}A{x}^2+C{y}^2+Dx+Ey+F=0\\ A=1,C=1,D=-2,E=0,F=-8\\ \mathrm{Here}A=C\ne 0\end{array}$

So the equation represents a circle.

Hence the matching graph is $2(a)$ .

Given equation is $2x^2-4x-3y-3=0$

  $\begin{array}{l}A{x}^2+C{y}^2+Dx+Ey+F=0\\ A=2,C=0,D=-4,E=-3,F=-3\\ \mathrm{Here}AC=0\end{array}$

So the equation represents a parabola.

Hence the matching graph is $3(d)$ .

Given equation is $x^2+6y^2-2x-5=0$

  $\begin{array}{l}A{x}^2+C{y}^2+Dx+Ey+F=0\\ A=1,C=6,D=-2,E=0,F=-5\\ \mathrm{Here}AC>0\end{array}$

So the equation represents a ellipse.

Hence the matching graph is $4(c)$ .

  $\begin{array}{l}A{x}^2+C{y}^2+Dx+Ey+F=0\\ A=1,C=6,D=-2,E=0,F=-5\\ \mathrm{Here}AC>0\end{array}$

Solution: Given equation is

• 1(b)
• 2(a)
• 3(d)
• 4(c)