A parabola can be drawn given a focus of ( 6 , − 5 ) (6,−5) and a directrix of y = 1 y=1. Write the equation of the parabola in
any form. -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12
1 answer:
Answer:
y = -(1/12)(x -6)² -2
Step-by-step explanation:
The vertex of the parabola is halfway between the focus and the directrix, so has y-coordinate (-5+1)/2 = -2. The difference in the y-coordinates between the focus and the vertex is ...
p = -5 -(-2) = -3
An equation of the parabola with vertex (h, k) and focus-vertex distance p can be written:
y = 1/(4p)(x -h)² +k
For (h, k) = (6, -2) and p = -3, the equation is ...
y = (-1/12)(x -6)² -2
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Answer:
a. Area = 1.94m²
b. Area = (p² + 0.5)m²
c. Height = 1.5m
Step-by-step explanation:
Given
<em>Let H represents Height and A represents Area</em>
<em>From the first and second statements, we have that:</em>
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<em>a. Calculating Area When Height = 1.2</em>
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<em>Substitute 1.2 for H</em>
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Hence, the area is 1.94m²
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<em>b. Calculating Area When Height = p</em>
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<em>Substitute p for H</em>
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Hence, the area is (p² + 0.5)m²
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c. <em>Calculating Height When Area = 2.75m</em>²
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<em>Substitute 2.75 for A</em>
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<em>Subtract 0.5 from both sides</em>
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<em>Take Square Root of both sides</em>
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Hence, the height is 1.5m