Asked by Person.
What is the equation of a parabola with the given vertex and focus?
Vertex: (1,6) Focus: (1,8)
Vertex: (1,6) Focus: (1,8)
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The vertex form of the equation of a parabola is (y-k) = a(x-h)^2, where (h,k) is the vertex, and the sign of "a" determines whether the parabola opens up or down.
In this case, the vertex is (1,6), so we have h = 1 and k = 6. Also, the focus is (1,8), so the parabola opens upward.
To find "a", we use the distance formula between the vertex and the focus, which is given by:
sqrt((y-k)^2 + (x-h)^2) = |a|(x-h)
Substituting the vertex and focus coordinates, we get:
sqrt((8-6)^2 + (1-1)^2) = |a|(1-1)
2 = 0
This is impossible, so there is no such parabola that satisfies the given vertex and focus.
In this case, the vertex is (1,6), so we have h = 1 and k = 6. Also, the focus is (1,8), so the parabola opens upward.
To find "a", we use the distance formula between the vertex and the focus, which is given by:
sqrt((y-k)^2 + (x-h)^2) = |a|(x-h)
Substituting the vertex and focus coordinates, we get:
sqrt((8-6)^2 + (1-1)^2) = |a|(1-1)
2 = 0
This is impossible, so there is no such parabola that satisfies the given vertex and focus.
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