Question

Can someone please help me solve the following?Please put numbers on graph

Answer 1

Given:

The equation of the hyperbola is given as,

`(y^2)/(25)-(x^2)/(4)=1........(1)^{}`

The objective is to graph the equation of the hyperbola.

Step-by-step explanation:

The general equation of hyperbola open in the vertical axis of up and down is,

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

Here, (h,k) represents the center of the hyperbola.

The focal length can be calculated as,

`c=\sqrt[]{a^2+b^2}\text{ . . . . (3)}`

On plugging the values of a and b in equation (3),

`\begin{gathered} c=\sqrt[]{5^2+2^2} \\ =\sqrt[]{25+4} \\ =\sqrt[]{29} \end{gathered}`

The foci can be calculated as,

`\begin{gathered} F(h,k\pm c)=F(0,0\pm\sqrt[]{29}) \\ =F(0,\pm\sqrt[]{29}) \end{gathered}`

The vertices can be calculated as,

`\begin{gathered} V(h,k\pm a)=V(0,0\pm5) \\ =V(0,\pm5) \end{gathered}`

To obtain graph:

The graph of the given hyperbola can be obtained as,

Hence, the graph of the given hyperbola is obtained.