Fabio is designing a flashlight that uses a parabolic reflecting mirror and a light source. the shape of the mirror can be modeled by (x-2)^2=10(y-3), where x and y are measured in inches. where is the focus of the flashlight? a. (–2, –0.5) b. (2, –5.5) c. (2, 5.5) d. (5.5, 2)

(2, 11/2)

Step-by-step explanation:

This is a vertical parabola; we know that because x is squared here, while y is not.  The standard equation of a vertical parabola with vertex (h,k) is

4p(y-k) = (x-h)^2, where p is the distance between the vertex and the focus.  Comparing

4p(y-k) = (x-h)^2 to

10(y-3)  = (x-2)^2, we see that 4p = 10.  Therefore, p = 10/4 = 5/2, which is the vertical distance between the focus and the vertex.

Since the coordinates of the vertex are easily read from the given equation

(x-2)^2=10(y-3):  (h,k) = (2, 3)

all we need to do is to add p (5/2) to the y-coordinate (3);

The focus is at (2, 3 + 5/2), or (2, 11/2).

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step-by-step explanation:

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column