the equation of the asymptotes of the hyperbola?:16y^2-9x^2=144 are ??
Show step plz
as you know the hyperbola
y^2/a^2 - x^2/b^2 = 1
has asymptotes x = ±b/a y
To find the equation of the asymptotes of a hyperbola, we need to examine the standard form equation of the hyperbola. The standard form equation for a hyperbola with its center at the origin (0,0) is:
(x^2/a^2) - (y^2/b^2) = 1
or
(y^2/b^2) - (x^2/a^2) = 1
where 'a' represents the distance from the center to the vertices along the x-axis, and 'b' represents the distance from the center to the vertices along the y-axis.
In your given equation, 16y^2 - 9x^2 = 144, we need to put it into the standard form by dividing both sides by 144:
(y^2/9) - (x^2/16) = 1
Now we can see that 'a' equals the square root of 16, which is 4, and 'b' equals the square root of 9, which is 3.
The equation of the asymptotes for a hyperbola of this form with the center at the origin (0,0) is given by:
y = (b/a) * x
and
y = -(b/a) * x
Substituting the values of 'a' and 'b' into these equations, we get:
y = (3/4) * x
and
y = -(3/4) * x
Therefore, the equations of the asymptotes for the hyperbola 16y^2 - 9x^2 = 144 are: y = (3/4) * x and y = -(3/4) * x.