Respuesta :
THe hyperbola is horizontally oriented.
c^2 = a^2 + b^2
34 = 9 + b^2
b^2 = 25
b = 5
x^2/9 - y^2/25 = 1
I hope that this is the answer that you were looking for and it has helped you.
c^2 = a^2 + b^2
34 = 9 + b^2
b^2 = 25
b = 5
x^2/9 - y^2/25 = 1
I hope that this is the answer that you were looking for and it has helped you.
Answer:
[tex]\frac{x^2}{9}-\frac{b^2}{25}=1[/tex]
Step-by-step explanation:
Since, we know that,
The equation of hyperbola,
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
Where, (h,k) is the center of the hyperbola,
Here, h = k = 0,
So, the equation of hyperbola is,
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1-----(1)[/tex]
Also, a = distance between center and vertices of hyperbola,
Given, vertices = (±3,0)
[tex]a=\sqrt{(0-3)^2+(0-0)^2}=\sqrt{9}=3[/tex]
[tex]\implies a^2 = 9[/tex]
Now, foci, c= (±√34,0),
Since, foci of hyperbola (1) is,
[tex](\pm\sqrt{a^2+b^2},0)[/tex]
[tex]\implies a^2+b^2= (\sqrt{34})^2[/tex]
[tex]\implies 3^2 + b^2 = 34[/tex]
[tex]\implies b^2 = 34 - 9 = 25[/tex]
Hence, the equation of the given hyperbola is,
[tex]\frac{x^2}{9}-\frac{b^2}{25}=1[/tex]
