Question

How to write the standard equation for the hyperbola that is on the graph

Answer 1

`=\text{ }(y^2)/(25)-(x^2)/(9)`Step-by-step explanation:

The standard form of the hyperbola:

`((y-k)^2)/(a^2)-((x-h)^2)/(b^2)\text{ = }1`

The center of the hyperbola is at (h, k) = The point where the lines intersect

(h, k) = (0, 0)

For hyperbola:

c² = a² + b²

b is gotten by tracing the value of a to the intersecting line. Trace 3 down to the x axis. you get 5.

`\begin{gathered} a\text{ = distance from center to vertex} \\ \text{the hyperbola coordinate = (0, a) = }(0,\text{ 3)} \\ \text{the other one = (0, -a) = (0, -3)} \\ \text{Hence, a = 3} \end{gathered}`
`\begin{gathered} c\text{ = distance from the center to the focus point} \\ b\text{ = 5 and -b = 5} \\ c^2=3^2+5^2 \end{gathered}`
`\begin{gathered} c^2\text{ = 9+25 = 34} \\ c\text{ = }\sqrt[]{34} \\ c\text{ = 5.83} \end{gathered}`

The equation becomes:

`\begin{gathered} ((y-k)^2)/(5^2)-((x-h)^2)/(3^2)=\text{ }((y-0)^2)/(5^2)-((x-0)^2)/(3^2) \\ =\text{ }(y^2)/(25)-(x^2)/(9) \end{gathered}`