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Lera25 [3.4K]
3 years ago
6

Derive the equation of the parabola with a focus at (-5,5) and a directix of y = -1

Mathematics
1 answer:
Paladinen [302]3 years ago
7 0

Answer:

D

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

\sqrt{(x+5)^2+(y-5)^2} = | y + 1 |

Squaring both sides

(x + 5)² + (y - 5)² = (y + 1)^2 , that is

(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides

(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify

y² + 2y + 1 - y² + 10y - 25 = (x + 5)²

12y - 24 = (x + 5)² ← factor left side

12(y - 2) = (x + 5)² ← divide both sides by 12

y - 2 = \frac{1}{12} (x + 5)² ← add 2 to both sides

y = \frac{1}{12} (x + 5)² + 2

or

f(x) = \frac{1}{12} (x + 5)² + 2 → D

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2 years ago
There are equal numbers of both red and black cards in a deck of 52.
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Each of those answers is a different way to figure the odds, they come out the same each time, as expected.

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+ Hint, when Penn Jillette asks you “is this your card” your card is always the 3 of clubs. So… 0% chance.

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