A farmer wants to build a rectangular garden 10ft long and 6ft wide. How many feet of fencing should he buy?
1 answer:
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Refer to the diagram shown below.
The distance, d, from the focus to a point P (x,y) is equal to the distance from the directrix to P.
Therefore
d² = (6 - y)²
= (x + 2)² + y²
That is,
36 - 12y + y² = (x + 2)² + y²
12y = -(x + 2)² + 36
The equation of the parabola is
y = -(1/12)(x + 2)² + 3
It may be written as
-12(y - 3) = (x + 2)²
The leading coefficient -1/12 is negative, therefore the curve opens downward.
Answer:
The equation is (x + 2)² = -12(y - 3).
The curve opens downward.
The distance, d, from the focus to a point P (x,y) is equal to the distance from the directrix to P.
Therefore
d² = (6 - y)²
= (x + 2)² + y²
That is,
36 - 12y + y² = (x + 2)² + y²
12y = -(x + 2)² + 36
The equation of the parabola is
y = -(1/12)(x + 2)² + 3
It may be written as
-12(y - 3) = (x + 2)²
The leading coefficient -1/12 is negative, therefore the curve opens downward.
Answer:
The equation is (x + 2)² = -12(y - 3).
The curve opens downward.