Center at (-4,-1) passes through (-2,3)

Hello from MrBillDoesMath!

(x+4)^2 + (y+1)^2 = 20

Discussion:

The equation of a circle with center (h,k) and radius "r" is given by

(x - h)^2 + (y-k)^2 = r^2.

As (-4, -1) is the center of the circle this equation becomes:

(x - (-4))^2 + (y - (-1))^2 = r^2  =>

(x+4)^2 + (y+1)^2 = r^2.

We need to determine the value of "r", the radius of the circle. The length of the radius is the distance between the center point and the point (-2,3) . It can be gotten using the Pythagorean theorem:

r^2  = (-4 - (-2)) ^2 + (-1 - 3)^2) =     (diff of x^2 + diff of y^2)

         (-4 +2) ^2 + (-4)^2  =

         (-2)^2       + 16)

         4              + 16

So the full equation is

(x+4)^2 + (y+1)^2 = 20

Thank you,

MrB

explanation:

infrared radiation has wavelength in the range between 700 nm and 1 mm. lets' convert these values into scientific notation, keeping in mind that:

let's start from the lower value, we have:

(we moved the dot two places to the left, so we increased the exponent by 2 units, from -9 to -7)

the higher value is:

so, the range of wavelength of infrared radiation is: