Question

Which equation represents the hyperbola in general form?

Answer 1

Answer: D. 9y2 − 4x2 − 36y + 16x − 16 = 0

Step-by-step explanation: I got this right on Edmentum.

Answer 2

D.

`9 {y}^(2) - 4 {x}^(2)- 36y + 16x - 16 = 0`

Step-by-step explanation

The standard equation of the hyperbola is

`\frac{ {(y - 2)}^(2) }{4} - \frac{ {(x - 2)}^(2) }{9} = 1`

We multiply through by 36 to obtain:

`9 {(y - 2)}^(2) - 4( {x - 2)}^(2) = 36`

We now expand to get,

`9( {y}^(2) - 4y + 4) - 4( {x}^(2) - 4x + 4) = 36`

Expand :

`9 {y}^(2) - 36y + 36 - 4 {x}^(2) + 16x - 16 = 36`

To get the general form, we equate everything to zero to get,

`9 {y}^(2) - 4 {x}^(2)- 36y + 16x - 16 = 0`

The correct choice is D.