Answer:
p=1
Step-by-step explanation:
20=20
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SOLUTION
From the question, the center of the hyperbola is
a is the distance between the center to vertex, which is -1 or 1, and
c is the distance between the center to foci, which is -2 or 2.
b is given as
![\begin{gathered} b^2=c^2-a^2 \\ b^2=2^2-1^2 \\ b=\sqrt[]{3} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20b%5E2%3Dc%5E2-a%5E2%20%5C%5C%20b%5E2%3D2%5E2-1%5E2%20%5C%5C%20b%3D%5Csqrt%5B%5D%7B3%7D%20%5Cend%7Bgathered%7D)
But equation of a hyperbola is given as
Substituting the values of a, b, h and k, we have
![\begin{gathered} \frac{(x-0)^2}{1^2}-\frac{(y-0)^2}{\sqrt[]{3}^2}=1 \\ \frac{x^2}{1}-\frac{y^2}{3}=1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%28x-0%29%5E2%7D%7B1%5E2%7D-%5Cfrac%7B%28y-0%29%5E2%7D%7B%5Csqrt%5B%5D%7B3%7D%5E2%7D%3D1%20%5C%5C%20%5Cfrac%7Bx%5E2%7D%7B1%7D-%5Cfrac%7By%5E2%7D%7B3%7D%3D1%20%5Cend%7Bgathered%7D)
Hence the answer is
Answer:
W=88
Step-by-step explanation:
4*(c-66)=c
4c-66*4=c
3c=66*4
c=22*4
c=88
w=88
OK, so the graph is a parabola, with points x=0,y=0; x=6,y=-9; and x=12,y=0
Because the roots of the equation are 0 and 12, we know the formula is therefore of the form
y = ax(x - 12), for some a
So put in x = 6
-9 = 6a(-6)
9 = 36a
a = 1/4
So the parabola has a curve y = x(x-12) / 4, which can also be written y = 0.25x² - 3x
The gradient of this is dy/dx = 0.5x - 3
The key property of a parabolic dish is that it focuses radio waves travelling parallel to the y axis to a single point. So we should arrive at the same focal point no matter what point we chose to look at. So we can pick any point we like - e.g. the point x = 4, y = -8
Gradient of the parabolic mirror at x = 4 is -1
So the gradient of the normal to the mirror at x = 4 is therefore 1.
Radio waves initially travelling vertically downwards are reflected about the normal - which has a gradient of 1, so they're reflected so that they are travelling horizontally. So they arrive parallel to the y axis, and leave parallel to the x axis.
So the focal point is at y = -8, i.e. 1 metre above the back of the dish.
