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icang [17]
3 years ago
12

Is there a relationship between area or perimeter of a rectangle

Mathematics
1 answer:
Arturiano [62]3 years ago
4 0
Hello,

For a given perimeter (P) there are an infinity of Area (A)
Let's say x the length, and y the wide of the rectangle

P=2(x+y)
A=xy
k=x-y >=0

As (x+y)²-4xy=(x-y)²: A²-4P=k² or P=(A²-k²)/4
In primus, you will find a graph (abacus) giving P for a A and k given.
Negative Area or P are excluded.(just remind the first quadrant, A>=0 and P>=0)

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Write the equation of a parabola with focus at (1,-4) and a directrix at X=2
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Answer:

The equation of a parabola is

x =  \frac{1}{4(f - h)} (y - k) ^{2}  + h

Step-by-step explanation:

(h,k) is the vertex and (f,k) is the focus.

Thus, f = 1, k = −4.

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.

Solving the system, we get h = 3/2, k = -4, f = 1.

The standard form is:

x =  -  \frac{y ^{2} }{2}  - 4y -  \frac{13}{2}

The general form is:

2x +  {y}^{2}  + 8y + 13 = 0

The vertex form is:

x =  -  \frac{(y + 4) ^{2} }{2}  +  \frac{3}{2}

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.

The focal length is the distance between the focus and the vertex: 1/2.

The focal parameter is the distance between the focus and the directrix: 1.

The latus rectum is parallel to the directrix and passes through the focus: x = 1.

The length of the latus rectum is four times the distance between the vertex and the focus: 2.

The eccentricity of a parabola is always 1.

The x-intercepts can be found by setting y = 0 in the equation and solving for x.

x-intercept:

( -  \frac{13}{2}  \: ,0)

The y-intercepts can be found by setting x = 0 in the equation and solving for y.

y-intercepts:

(0, - 4 -  \sqrt{3)}

(0, - 4 +  \sqrt{3)}

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Answer:

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Step-by-step explanation:

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