Question

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

xy=-2.5

Answer 1

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

The correct option is b

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=(B)/(A-C)`

`\tan 2\theta=(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.