Hyperbolic Mirror A hyperbolic mirror (used in some telescopes) has the property that a light ray directed at the focus will be reflected to the other focus. The mirror in the figure has the equation x 2 36 − y 2 64 = 1 At which point on the mirror will light from the point (0, 10) be reflected to the other focus?
Hyperbolic Mirror A hyperbolic mirror (used in some telescopes) has the property that a light ray directed at the focus will be reflected to the other focus. The mirror in the figure has the equation x 2 36 − y 2 64 = 1 At which point on the mirror will light from the point (0, 10) be reflected to the other focus?
Solution Summary: The author calculates the point where the line will be deflected to the other focus.
Hyperbolic Mirror A hyperbolic mirror (used in some telescopes) has the property that a light ray directed at the focus will be reflected to the other focus. The mirror in the figure has the equation
x
2
36
−
y
2
64
=
1
At which point on the mirror will light from the point (0, 10) be reflected to the other focus?
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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