Question

What are the equations of the asymptotes of this parabola?
x^2/25 - y^2/4 =1

Answer 1

This is not a parabola, its an hyperbola.

For the general eqtn x^2/a^2 - y^2/b^2 =1
the asymptotes are y = (-b/a)x & (b/a)x

Answer 2

h=0, k=0, a=5, b=2

slopes of asymptotes:
m₁= b/a=2/5
m₂= -b/a= -2/5

The asymptotes pass through the center of the hyperbola. Use the center point to determine the y-intercepts of the asymptotes.
center (h,k) = (0,0)

y-intercept₁ = k - m₁h
= 0 - (2/5)(0)
= 0

y-intercept₂ = 0 - (-2/5)(0)
= 0

asymptote₁: y = (2/5)x
asymptote₂: y = (-2/5)x