Answer:
D.
![\frac{y^2}{12}-\frac{x^2}{6}=1](https://tex.z-dn.net/?f=%5Cfrac%7By%5E2%7D%7B12%7D-%5Cfrac%7Bx%5E2%7D%7B6%7D%3D1)
Step-by-step explanation:
we are given
we can use standard equation of hyperbola
![\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-k%29%5E2%7D%7Ba%5E2%7D-%5Cfrac%7B%28x-h%29%5E2%7D%7Bb%5E2%7D%3D1)
where
center=(h,k)
center at origin
so, h=0 and k=0
vertex is
![(0,\sqrt{12})](https://tex.z-dn.net/?f=%280%2C%5Csqrt%7B12%7D%29)
we can use formula
vertices: (h, k + a)
we get
![k+a=\sqrt{12}](https://tex.z-dn.net/?f=k%2Ba%3D%5Csqrt%7B12%7D)
we can plug k=0
![a=\sqrt{12}](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B12%7D)
now, we can plug these values
![\frac{(y-0)^2}{(\sqrt{12})^2}-\frac{(x-0)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-0%29%5E2%7D%7B%28%5Csqrt%7B12%7D%29%5E2%7D-%5Cfrac%7B%28x-0%29%5E2%7D%7Bb%5E2%7D%3D1)
now, we are given it passes through ![(2\sqrt{3} ,6)](https://tex.z-dn.net/?f=%282%5Csqrt%7B3%7D%20%2C6%29)
so, we have
![x=2\sqrt{3},y=6](https://tex.z-dn.net/?f=x%3D2%5Csqrt%7B3%7D%2Cy%3D6)
we can plug these values and then we can solve for b
![\frac{(6-0)^2}{(\sqrt{12})^2}-\frac{(2\sqrt{3}-0)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%286-0%29%5E2%7D%7B%28%5Csqrt%7B12%7D%29%5E2%7D-%5Cfrac%7B%282%5Csqrt%7B3%7D-0%29%5E2%7D%7Bb%5E2%7D%3D1)
and we get
![36b^2-144=12b^2](https://tex.z-dn.net/?f=36b%5E2-144%3D12b%5E2)
we can solve for b
and we get
![b=\sqrt{6}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B6%7D)
now, we can plug these values
![\frac{(y-0)^2}{(\sqrt{12})^2}-\frac{(x-0)^2}{(\sqrt{6})^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28y-0%29%5E2%7D%7B%28%5Csqrt%7B12%7D%29%5E2%7D-%5Cfrac%7B%28x-0%29%5E2%7D%7B%28%5Csqrt%7B6%7D%29%5E2%7D%3D1)
we can simplify it
and we get
![\frac{y^2}{12}-\frac{x^2}{6}=1](https://tex.z-dn.net/?f=%5Cfrac%7By%5E2%7D%7B12%7D-%5Cfrac%7Bx%5E2%7D%7B6%7D%3D1)
Answer:
I can’t see the picture well please make it more detailed
Step-by-step explanation:
Answer:
The value of m is 3
Step-by-step explanation:
we have
![x^{2}+mx+n=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2Bmx%2Bn%3D0)
step 1
Find the value of n
For x=0
![0^{2}+m(0)+n=0](https://tex.z-dn.net/?f=0%5E%7B2%7D%2Bm%280%29%2Bn%3D0)
![n=0](https://tex.z-dn.net/?f=n%3D0)
step 2
Find the value of m
For x=-3
substitute
![x^{2}+mx=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%2Bmx%3D0)
![(-3)^{2}+m(-3)=0](https://tex.z-dn.net/?f=%28-3%29%5E%7B2%7D%2Bm%28-3%29%3D0)
![9-3m=0](https://tex.z-dn.net/?f=9-3m%3D0)
![3m=9](https://tex.z-dn.net/?f=3m%3D9)
![m=3](https://tex.z-dn.net/?f=m%3D3)
The answer is -3 yea it is that it is -3