This ODE is separable, so you can write
Integrating both sides gives
and given the initial condition
, you have
so that the solution is
Integrating both sides gives
and given the initial condition
so that the solution is
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1 answer:
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Answer:
a) The axis of symmetry is the line, y = 2
b) The vertex of a parabola is (-3, 2)
c) The focus of the parabola is (0, 2)
d) The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola
Step-by-step explanation:
a) The function for the parabola can be expressed as follows;
12·(x + 3) = (y - 2)²
The general form of the equation of the parabola is x = a·(y - k)² + h
The axis of symmetry is the line, y = k
By comparison, with the given equation of the parabola, we have;
12·(x + 3) = (y - 2)²
x = (1/12)·(y - 2)² - 3
Therefore;
a = (1/12), k = 2, h = -3
The axis of symmetry is y = k
∴ The axis of symmetry is the line, y = 2
b) The vertex of a parabola = (h, k)
∴ The vertex of a parabola = (-3, 2)
c) The focus of a parabola is
Therefore, the focus of the parabola is = (0, 2)
The focus of the parabola = (0, 2)
d) The directrix of a parabola is
The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel
