10. What are the equations of the asymptotes for the hyperbola?:
(x^2/9)-(y^2/25)=1
A. y = ±5/3x
B. y = ±3/5x
C. y = ±9/25x
D. y = ±5/4x
To find the equations of the asymptotes for a hyperbola, you need to use the standard form equation of the hyperbola, which is given by (x^2/a^2) - (y^2/b^2) = 1 for a hyperbola with a vertical transverse axis (meaning the x^2 term comes before the y^2 term).
Comparing this with the given equation (x^2/9) - (y^2/25) = 1, we can see that a = 3 and b = 5.
The equations of the asymptotes for a hyperbola are given by y = ±(b/a)x. Plugging in the values of a and b, we get:
y = ±(5/3)x
So the correct answer is A. y = ±5/3x.