Which of these transformations are isometries?
1 answer:
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Answer:
Step-by-step explanation:
Given:
Focus point = (-5, -4)
Vertex point = (-5, -3)
We need to find the equation for the parabola.
Solution:
Since the x-coordinates of the vertex and focus are the same,
so this is a regular vertical parabola, where the x part is squared. Since the vertex is above the focus, this is a right-side down parabola and p is negative.
The vertex of this parabola is at (h, k) and the focus is at (h, k + p). So, directrix is y = k - p.
Substitute y = -4 and k = -3.
So the standard form of the parabola is written as.
Substitute vertex (h, k) = (-5, -3) and p = -1 in the above standard form of the parabola.
So the standard form of the parabola is written as.
Therefore, equation for the parabola with focus at (-5,-4) and vertex at (-5,-3)