B-ball network uses a parabolic microphone to capture all the sounds from the basketball players and coaches during each regular season game. If one of its microphones has a parabolic surface generated by the parabola 18y=x^2, locate the focus (electronic receiver) of the parabola.
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18y = x²
y = 1/18 x²
Since the equation is y as a function of x, it graphs as a vertical parabola and, since the sign of the 'a' term is positive, it opens upward, which puts the focus above the vertex.
Since there is no 'b' or 'c' term, there is no translation, so the vertex is at (0, 0):
h = 0
k = 0
a = 1/18
p = 1 / 4a
p = 1 / 4(1/18)
p = 1 / (4/18)
p = 1 / (2/9)
p = 9/2
Focus (h, k + p)
Focus (0, 0 + 9/2)
Focus (0, 9/2), or
Focus (0, 4.5)
¯¯¯¯¯¯¯¯¯¯¯¯
y = 1/18 x²
Since the equation is y as a function of x, it graphs as a vertical parabola and, since the sign of the 'a' term is positive, it opens upward, which puts the focus above the vertex.
Since there is no 'b' or 'c' term, there is no translation, so the vertex is at (0, 0):
h = 0
k = 0
a = 1/18
p = 1 / 4a
p = 1 / 4(1/18)
p = 1 / (4/18)
p = 1 / (2/9)
p = 9/2
Focus (h, k + p)
Focus (0, 0 + 9/2)
Focus (0, 9/2), or
Focus (0, 4.5)
¯¯¯¯¯¯¯¯¯¯¯¯