Respuesta :
Answer:
The equation of the hyperbola is presented as follows;
[tex]\frac{x^2}{16} - \frac{y^2}{9} =1[/tex]
Step-by-step explanation:
Here we have the standard equation of an hyperbola given as follows;
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} =1[/tex]
Where:
a = x intercept
The asymptote is ±(b/a)x
Since the intercept, a is ± 4, the vertices are (-4, 0) and (4, 0)
We are given the asymptote as y = 3/4x, therefore, since the genral form of the asymptote is ±(b/a)x, comparing, we have;
±(b/a)x ≡ 3/4x
We have a = ±4, therefore, b = 3
Hence the equation of the hyperbola is found by putting in the values of a and b in the general form as follows;
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} =1 \Rightarrow \frac{x^2}{4^2} - \frac{y^2}{3^2} =1[/tex]
The equation of the hyperbola = x²/16 - y²/9 = 1.
