Question

Identify the equation or coordinates of the following conic and its equation.

Answer 1

X²/16 +y²/9 =1
(General formula: (x-h)²/a² -(y-k)²/b²). since h=k=0, it becomes x²/a² -y²/b²=1)

In your function a =4 & b =3. Since a>b this hyperbola opens right & left
The equation of the asymptotes are:
y₁=k+b/a(x-h) & y₂=k-b/a(x-h), but since h=k=0 then:
y₁=(b/a)x  &  y₂= -(b/a)x
Or y₁=3/4x & y₂= -3/4x (these 2 are the equations of the asymptotes