Question 554815
Graph and show the asymptotes: x^2/9-y^2/49=1
**
x^2/9-y^2/49=1
This is an equation of a hyperbola with horizontal transverse axis of the standard form:
(x-h)^2-(y-k)^2=1, with (h,k) being the (x,y) coordinates of the center
For given equation:
center: (0,0)
a^2=9
a=√9=3
b^2=49
b=√49=7
slope of asymptotes=±b/a=±7/3
asymptotes are two straight lines with slopes 7/3 and -7/3, both going thru the center at (0,0)
Equation of asymptotes: y=7x/3 and y=-7x/3
See graph below:
y=±(49x^2/9-49)^.5
{{{ graph( 300, 300, -10, 10, -10, 10,(49x^2/9-49)^.5,-(49x^2/9-49)^.5,7x/3,-7x/3) }}}