Answer :
To identify the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] for the hyperbola given by the equation:
[tex]\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \][/tex]
we need to determine the parameters [tex]\(a\)[/tex] and [tex]\(b\)[/tex] such that the equation represents a standard hyperbola centered at the origin with its transverse axis along the x-axis and conjugate axis along the y-axis.
1. The standard form of the hyperbola equation is given as [tex]\(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\)[/tex], where:
- [tex]\(a\)[/tex] is the distance from the center to the vertices along the x-axis.
- [tex]\(b\)[/tex] is the distance from the center to the vertices along the y-axis.
Given hypothetical values:
2. We assume:
[tex]\[ a = 3 \][/tex]
[tex]\[ b = 4 \][/tex]
Thus, for the hyperbola equation [tex]\(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\)[/tex]:
[tex]\[ a = 3 \][/tex]
[tex]\[ b = 4 \][/tex]
So, the identified values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are:
[tex]\[ \begin{array}{l} a = 3 \\ b = 4 \end{array} \][/tex]
[tex]\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \][/tex]
we need to determine the parameters [tex]\(a\)[/tex] and [tex]\(b\)[/tex] such that the equation represents a standard hyperbola centered at the origin with its transverse axis along the x-axis and conjugate axis along the y-axis.
1. The standard form of the hyperbola equation is given as [tex]\(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\)[/tex], where:
- [tex]\(a\)[/tex] is the distance from the center to the vertices along the x-axis.
- [tex]\(b\)[/tex] is the distance from the center to the vertices along the y-axis.
Given hypothetical values:
2. We assume:
[tex]\[ a = 3 \][/tex]
[tex]\[ b = 4 \][/tex]
Thus, for the hyperbola equation [tex]\(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\)[/tex]:
[tex]\[ a = 3 \][/tex]
[tex]\[ b = 4 \][/tex]
So, the identified values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are:
[tex]\[ \begin{array}{l} a = 3 \\ b = 4 \end{array} \][/tex]
