Derive the equation of the ellipse with foci at (1,0) and (−1,0) whose distance between vertices is 6. Make a picture to help. Label the foci, and place and label a point (x, y) along the ellipse. Draw the focal distances from the point (x, y) to each focus point.

Hint: Note that the endpoints on the major axis are often called vertices (the other endpoints on the minor axis are called co-vertices).

Use the fact that the distance between the vertices is equal to the sum of the focal distances. Use the distance formula to start.

Put the steps in order:

step-by-step explanation:

compare

answer: 40392

step-by-step explanation:

10098 x 4 = 40392

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.