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svetoff [14.1K]
3 years ago
11

Which equation represents the hyperbola in general form?

Mathematics
1 answer:
valina [46]3 years ago
7 0

ANSWER

D.

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

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.

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