Question

Find the equation of the hyperbola centered at the origin that satisfies the given conditions: x-intercepts = +,-4 and asymptote at y=3/4x

Answer 1

B

Explanation:

edge

Answer 2

The equation of the hyperbola is presented as follows;

`(x^2)/(16) - (y^2)/(9) =1`

Explanation:

Here we have the standard equation of an hyperbola given as follows;

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

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;

`(x^2)/(a^2) - (y^2)/(b^2) =1 \Rightarrow (x^2)/(4^2) - (y^2)/(3^2) =1`

The equation of the hyperbola = x²/16 - y²/9 = 1.