Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. f(x) = −one eighth (x − 2)2 + 6 f(x) = one eighth (x − 2)2 + 6 f(x) = −one eighth (x + 2)2 + 8 f(x) = one eighth (x + 2)2 + 8
2 answers:
Answer: f(x) = −one eighth (x − 2)2 + 6
Answer:
A
Step-by-step explanation:
For any point (x, y ) on the parabola the focus and directrix are equidistant
Using the distance formula
= | y - 8 |
Squaring both sides gives
(x - 2)² + (y - 4)² = (y - 8)²
(x - 2)² + y² - 8y + 16 = y² - 16y + 64 ( rearrange and simplify )
(x - 2)² = - 8y + 48
8y = - (x - 2)² + 48
y = - (x - 2)² + 6 → A
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Step-by-step explanation:
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60
Step-by-step explanation:
6x10=60
Assuming the length is y and the width is x Perimeter = y + y + x + x = 2y +2x = 2 (y + x) if the is 8 and the perimeter is 108 108 = 2 (y +8) 108/2 = y+8 54 = y +8 54 - 8 = y 46 = y Length = 46 inches