Question

When the equation of the hyperbola: 25x^2-16y^2=400 is written in standard form:\frac{(x-h)^2}{a^2} -\frac{(y-k)^2}{b^2}=1The value for h is AnswerThe value for k is AnswerThe value for a is AnswerThe value for b is Answer

Answer 1

Given the following equation of the hyperbola:

`25x^2-16y^2=400`

The standard form of the hyperbola will be as follows:

`((x-h)^2)/(a^2)-((y-k)^2)/(b^2)=1`

We will rewrite the given equation to be like the standard form:

`\begin{gathered} 25x^2-16y^2=400\rightarrow(/400) \\ (25x^2)/(400)-(16y^2)/(400)=(400)/(400) \\ \\ (x^2)/(16)-(y^2)/(25)=1 \\ \\ (x^2)/(4^2)-(y^2)/(5^2)=1 \end{gathered}`

Compare the last equation with the standard form:

So, the answer will be as follows:

The value of h = 0

The value of k = 0

The value of a = 4

The value of b = 5