SOLUTION: hallar la ecuacion de las hiperbolas determinadas por:
1) vertices (+-1,0) asÃntotas y=+-5x
2) focos (0,+-6) pasa por P=(-5,9)
3) focos (0,+-1) longitud eje real:1
4) asÃntot
Question 1133039: hallar la ecuacion de las hiperbolas determinadas por:
1) vertices (+-1,0) asÃntotas y=+-5x
2) focos (0,+-6) pasa por P=(-5,9)
3) focos (0,+-1) longitud eje real:1
4) asÃntotas y= +- x/2 pasa por el punto de coordenadas (5,2) Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Standard form: ->Transverse axis is horizontal
-.>Transverse axis is vertical
1)
given:
Vertices: (,), (,) =>Semi-major axis length:
First asymptote:
Second asymptote:
=> Transverse axis is vertical
Standard form:
intersection of the asymptotes is at origin:
so, center is at: (,) => and
=>
From the original equations of asymptotes, you can determine the slopes of the asymptotes to be and
since and , we have
=>
2.
2) focos (0,+-6) pasa por P=(-5,9)
the coordinates of the foci are (,±)
foci lie on y axis, so your formula is:
=> or
P=(,)
The distance formula is . Plug in the numbers,
The distance is 5.8309518948453.
=> round it to
3) focos (0,+-1) longitud eje real:1
longitud eje real:1=> the length transverse axis is
=>
=>
the coordinates of the foci are (,±) => =± and
foci lie on axis, so your formula is
=> or
4) asÃntotas = ± pasa por el punto de coordenadas (5,2)
= ±
intersection of the asymptotes is at origin:
so, center is at: (,) => and
asymptotesup-down = ±
since passes through (,)