Find equations for the asymptotes of the hyperbola x2/9 - y2/81 = 1
Rewrite the equation as
(x/3)^2 - (y/9)^2 = 1
When both x and y are very large in absolute value, the "1" on the right is negligible in comparison, so y/9 approaches +/- x/3
The asymptotes are therefore
y = 3x and y = -3x.
To find the equations of the asymptotes of the hyperbola, we can use the standard form equation:
(x/3)^2 - (y/9)^2 = 1
In general, the equations of the asymptotes for a hyperbola in standard form are given by:
y = ±(a/b)x
where "a" is the coefficient of x in the numerator of the x-term, and "b" is the coefficient of y in the numerator of the y-term.
In this case, a = 3 and b = 9, so the equations of the asymptotes of the hyperbola are:
y = (3/9)x = (1/3)x
and
y = -(3/9)x = -(1/3)x
Therefore, the equations of the asymptotes of the hyperbola x^2/9 - y^2/81 = 1 are:
y = (1/3)x and y = -(1/3)x.
To find the equations for the asymptotes of the hyperbola, we first need to rewrite the equation in standard form. The given equation is:
(x^2/9) - (y^2/81) = 1
Let's rearrange this equation to isolate x^2/9:
x^2/9 = 1 + y^2/81
Next, we can multiply both sides of the equation by 9 to get rid of the fraction:
x^2 = 9 + (9/81)y^2
Simplifying further:
x^2 = 9 + (1/9)y^2
Now, let's rewrite this equation in terms of (x/3) and (y/9):
(x/3)^2 - (y/9)^2 = 1
Notice that when x and y are both very large in absolute value, the "1" on the right side of the equation becomes negligible in comparison. In this case, y/9 approaches ±(x/3).
Therefore, the equations for the asymptotes are:
y = 3x
y = -3x