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

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

Using this, we can write the equation given as:

[tex](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[/tex]

So, B is the right answer.

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kudzordzifrancis kudzordzifrancis · Answer 2 · 2019-04-05T20:47:36+02:00

Answer:

b. [tex]x^2-y^2+8x+4y+3=0[/tex]

Step-by-step explanation:

The given hyperbola has equation [tex]x^2-y^2=9[/tex].

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;

[tex](x+4)^2-(y-2)^2=9[/tex]

We now expand to obtain;

[tex]x^2+8x+16-(y^2-4y+4)=9[/tex]

[tex]\Rightarrow x^2+8x+16-y^2+4y-4-9=0[/tex]

[tex]\Rightarrow x^2-y^2+8x+4y-4-9+16=0[/tex]

The correct choice is B.

[tex]\Rightarrow x^2-y^2+8x+4y+3=0[/tex]