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We'll first clear a few points.
1. A hyperbola with horizontal axis and centred on origin (i.e. foci are centred on the x-axis) has equation
x^2/a^2-y^2/b^2=1
(check: when y=0, x=+/- a, the vertices)
The corresponding hyperbola with vertical axis centred on origin has equation
y^2/a^2-x^2/b^2=1
(check: when x=0, y=+/- a, the vertices).
The co-vertex is the distance b in the above formula, such that
the distance of the foci from the origin, c satisfies c^2=a^2+b^2.
The rectangle with width a and height b has diagonals which are the asymptotes of the hyperbola.
We're given vertex = +/- 3, and covertex=+/- 5.
And since vertices are situated at (3,0), and (-3,0), they are along the x-axis.
So the equation must start with
x^2/3^2.
It will be good practice for you to sketch all four hyperbolas given in the choices to fully understand the basics of a hyperbola.
Answer:
perimeter = 107.4 m
area = 640.82 m²
Step-by-step explanation:
The line connecting the the centers of the adjacent sides of the garden is 20 m long. The line is a diagonal that forms an hypotenuse sides of a triangle.
The length of side of the rectangle has a ratio of 1 : 2. This means one side has a length a meters and the other 2a meters.
Pythagoras theorem can be use to get a since a right angle is formed due to the diagonal.
(a/2)² + (2a/2)² = 20²
(a/2)² + (a)² = 20²
a²/4 + a² = 400
(a² + 4a²)/4 = 400
5a²/4 = 400
cross multiply
5a² = 1600
a² = 1600/5
a² = 320
square root both sides
a = √320
a = 17.88854382
a ≈ 17.90
The required length is a = 17.90 m and the other side will be 17.90 × 2 = 35.80 m.
Area = length × breadth
area = 17.90 × 35.80 = 640.82 m²
perimeter = 2(l + b)
perimeter = 2(35.80 + 17.90)
perimeter = 2(53.7)
perimeter = 107.4 m
Answer:
X =2
Step-by-step explanation:
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