Question

Identify the equation of the translated graph in general form x^2-y^2=9 for T(-4,2)

Answer 1

B

Explanation:

If an equation of the form
`x^2-y^2=a` goes through a translation T (p,q), the transformed equation has the form
`(x-p)^2-(y-q)^2=a`

Using this, we can write the equation given as:

`(x-(-4))^2-(y-2)^2=9\\(x+4)^2-(y-2)^2=9\\x^2+8x+16-y^2+4y-4-9=0\\x^2-y^2+8x+4y+3=0`

So, B is the right answer.

Answer 2

b.
`x^2-y^2+8x+4y+3=0`

Explanation:

The given hyperbola has equation
`x^2-y^2=9`.

This hyperbola is centered at the origin.

If this hyperbola is translated, so that its center is now at (-4,2), its equation now becomes;

`(x+4)^2-(y-2)^2=9`

We now expand to obtain;

`x^2+8x+16-(y^2-4y+4)=9`

`\Rightarrow x^2+8x+16-y^2+4y-4-9=0`

`\Rightarrow x^2-y^2+8x+4y-4-9+16=0`

The correct choice is B.

`\Rightarrow x^2-y^2+8x+4y+3=0`