Answer:
Step-by-step explanation:
focus distance=9
a=2 f²=a²+b² ==> b²=9²-2²=77 ==> b=√77
[tex]\dfrac{(x-0)^2}{2^2}- \dfrac{(y-0)^2}{77}=1\\\\\\\boxed{\dfrac{x^2}{4}- \dfrac{y^2}{77}=1}\\[/tex]
Equation of hyperbola is [tex]\frac{x^{2} }{4} -\frac{y^{2} }{77} =1[/tex].
Hyperbola is defined as an open curve having two branches which are mirror images to each other.
A plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.
Given
Foci: (-9, 0) and (9, 0)
Foci: (±9, 0)
Vertices: (-2,0) and (2,0)
Vertices: (±2, 0)
So, a = ±2, c = ±9
Now [tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]b^{2} =c^{2} -a^{2}[/tex]
[tex]b^{2} =9^{2} -2^{2}[/tex]
[tex]b^{2} =81-4[/tex]
[tex]b^{2} =77[/tex]
Equation of hyperbola is
[tex]\frac{x^{2} }{a^{2} } -\frac{y^{2} }{b^{2} } =1[/tex]
⇒ [tex]\frac{x^{2} }{4} -\frac{y^{2} }{77} =1[/tex]
Hence, equation of hyperbola is [tex]\frac{x^{2} }{4} -\frac{y^{2} }{77} =1[/tex].
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