ANSWER
D.
![9 {y}^{2} - 4 {x}^{2}- 36y + 16x - 16 = 0](https://tex.z-dn.net/?f=9%20%7By%7D%5E%7B2%7D%20%20-%204%20%7Bx%7D%5E%7B2%7D-%2036y%20%2B%2016x%20-%2016%20%3D%200)
EXPLANATION
The standard equation of the hyperbola is
![\frac{ {(y - 2)}^{2} }{4} - \frac{ {(x - 2)}^{2} }{9} = 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%28y%20-%202%29%7D%5E%7B2%7D%20%7D%7B4%7D%20%20-%20%20%5Cfrac%7B%20%7B%28x%20-%202%29%7D%5E%7B2%7D%20%7D%7B9%7D%20%20%3D%201)
We multiply through by 36 to obtain:
![9 {(y - 2)}^{2} - 4( {x - 2)}^{2} = 36](https://tex.z-dn.net/?f=9%20%7B%28y%20-%202%29%7D%5E%7B2%7D%20%20-%204%28%20%7Bx%20-%202%29%7D%5E%7B2%7D%20%20%3D%2036)
We now expand to get,
![9( {y}^{2} - 4y + 4) - 4( {x}^{2} - 4x + 4) = 36](https://tex.z-dn.net/?f=9%28%20%7By%7D%5E%7B2%7D%20%20-%204y%20%2B%204%29%20-%204%28%20%7Bx%7D%5E%7B2%7D%20%20-%204x%20%2B%204%29%20%3D%2036)
Expand :
![9 {y}^{2} - 36y + 36 - 4 {x}^{2} + 16x - 16 = 36](https://tex.z-dn.net/?f=9%20%7By%7D%5E%7B2%7D%20%20-%2036y%20%2B%2036%20%20-%204%20%7Bx%7D%5E%7B2%7D%20%20%2B%2016x%20-%2016%20%3D%2036)
To get the general form, we equate everything to zero to get,
![9 {y}^{2} - 4 {x}^{2}- 36y + 16x - 16 = 0](https://tex.z-dn.net/?f=9%20%7By%7D%5E%7B2%7D%20%20-%204%20%7Bx%7D%5E%7B2%7D-%2036y%20%2B%2016x%20-%2016%20%3D%200)
The correct choice is D.
Answer:
8/10, 12/15, 16/20 and so on
Step-by-step explanation:
4x2/5x2 = 8/10
4x3/5x3 = 12/15
4x4/5x4 = 16/20 and so on
The required equation of the line is y = -1/2x
<h3>Equation of a line</h3>
The standard equation of a line is expressed as y = mx + b
- where:
- m is the slope
- b is the y intercept
Given the coordinate points (0,0) and (4, -2)
Slope = -2/4 = -1/2
The intercept is 0 since the line pass through the origin
Hence the required equation of the line is y = -1/2x
Learn more on equation of a line here: brainly.com/question/13763238
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