Identify the line(s) of symmetry for the conic section x-(y-1)^2=2
I have this... (Y-1)^2=(x-2) Vertex (2,1) Symmetry y=1. Is this correct?
right on.
To identify the line(s) of symmetry for the conic section given by the equation x - (y - 1)^2 = 2, you need to analyze the equation.
The given equation represents a parabola because of the squared term (y - 1)^2. However, the equation is in an unusual form.
To make it easier to identify the line of symmetry, let's rearrange the equation:
x - (y - 1)^2 = 2
First, we can simplify the equation by expanding the square term:
x - (y^2 - 2y + 1) = 2
Next, move the constant term (2) to the left side:
x - y^2 + 2y - 3 = 0
Now that we have the equation in standard form, we can determine the line(s) of symmetry.
For a parabola in standard form (x - h)^2 = 4p(y - k), the vertex is given by (h, k), and the line of symmetry is the vertical line x = h.
In this case, the equation has the form x - (y - 1)^2 = 2. Comparing it to standard form, we can see that:
h = 0 (since x - (y - 1)^2 is equivalent to x - 0(y - 1)^2)
k = 0 (since 2 in the standard form is equivalent to -2 in the given equation)
Therefore, the vertex is (0, 0), and the line of symmetry is x = 0, which is the y-axis.
So, the correct line of symmetry for the given conic section is the equation x = 0, which represents the y-axis.