Asymptotes y=4/3x, y=-4/3x, one vertex (3,0)

gebuiteldmz
2022-10-02
Answered

Find the equation of a hyperbola satisfying the given conditions.

Asymptotes y=4/3x, y=-4/3x, one vertex (3,0)

Asymptotes y=4/3x, y=-4/3x, one vertex (3,0)

You can still ask an expert for help

Piper Pruitt

Answered 2022-10-03
Author has **9** answers

The origin of Hyperbola is (0,0) that in centre, with vertex (3,0)

The standard equation for a hyperbola is

$$\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1$$

Now, as the vertex is (3,0) which gives:

a=3

Further, Asymptotes are given as

$$y=+\frac{4}{3}x\text{and}y=-\frac{4}{3}x\phantom{\rule{0ex}{0ex}}\text{or}y=\pm \frac{4}{3}x$$

Hence slope of the Asymptotes =b/a

equation of Hyperbola is

$$\frac{{x}^{2}}{9}-\frac{{y}^{2}}{16}=1$$

The standard equation for a hyperbola is

$$\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1$$

Now, as the vertex is (3,0) which gives:

a=3

Further, Asymptotes are given as

$$y=+\frac{4}{3}x\text{and}y=-\frac{4}{3}x\phantom{\rule{0ex}{0ex}}\text{or}y=\pm \frac{4}{3}x$$

Hence slope of the Asymptotes =b/a

equation of Hyperbola is

$$\frac{{x}^{2}}{9}-\frac{{y}^{2}}{16}=1$$

asked 2021-05-13

A movie stuntman (mass 80.0kg) stands on a window ledge 5.0 mabove the floor. Grabbing a rope attached to a chandelier, heswings down to grapple with the movie's villian (mass 70.0 kg), whois standing directly under the chandelier.(assume that thestuntman's center of mass moves downward 5.0 m. He releasesthe rope just as he reaches the villian).

a) with what speed do the entwined foes start to slide acrossthe floor?

b) if the coefficient of kinetic friction of their bodies withthe floor is 0.250, how far do they slide?

asked 2020-10-18

Find a least squares solution of Ax=b by constructing and solving the normal equations.

$A=\left[\begin{array}{cc}3& 1\\ 1& 1\\ 1& 4\end{array}\right],b\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

$\stackrel{\u2015}{x}=$ ?

asked 2021-09-26

Solve the equation: $2{x}^{2}-x-3=0$

asked 2021-09-28

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify.

asked 2021-12-21

Find an equation of the tangent line to the curve at the given point.

$y=\sqrt{x}(81,9)$

asked 2021-09-27

Solve the equation.

$27}^{x-1}={9}^{2x-3$

asked 2022-09-02

You sell a ring for $25. You originally bought the ring for $32. Use this information and the equation S=C + P (where S is the selling price, C is the cost, and P is the profit) to find out profit.