Question

Identify the graph of the equation. What is the angle of rotation for the equation?

xy=-2.5

Answer 1

Answer:

It is B. hyperbola, 45 degrees.

SteIt is p-by-step explanation:

If we rotate the standard form  x^2 - y^2 = 1 through 45 degrees we get xy = 1/2.

xy = -2.5 comes from x^2 - y^2 = -5  being rotated 45 degrees.

Answer 2

Answer:

The correct option is b

Step-by-step explanation:

The given equation is

$xy=-2.5$

It can be written as

$xy+2.5=0$              .... (1)

The general forms of conic is

$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$             .... (2)

From (1) and (2), we get

$A=0,B=1,C=0,D=0,E=0,E=2.5$

$B^2-4AC=1-4(0)(0)=1>0$

Since the value of B²- 4AC > 0, then it is hyperbola.

The formula form angle of rotation is

$\tan 2\theta=\frac{B}{A-C}$

$\tan 2\theta=\frac{1}{0-0}$

$\tan 2\theta=\infty$

$\tan 2\theta=\tan (90^{\circ})$

$2\theta=90^{\circ}$

$\theta=45^{\circ}$

The angle of rotation is 45°. Therefore the correct option is b.