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

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

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: