60. Find r so that the line through 12, 62 and 1-4, r2 is (a) parallel to 2x - 3y = 4 (b) perpendicular to x + 2y = 1.

Answer 1

(12,62) (1-4, r^2) have a line through them with slope = (66-r^2)/15= (y-62)/(x-12)

y= (66-r^2)x/15 +12r^2/15 -66(12)/15 -62

66-r^2/15 is the slope

2x-3y =4

3y= 2x-4

y = 2x/3 -4/3 is a line with slope 2/3. Any parallel line also has to have the same slope = 2/3

set (66-r^2)/15 = 2/3

66-r^2 = 10

r^2 = 56

r = sqr56 = 2sqr14 or -2sqr14

x+2y = 1

2y=-x+1

y =-x/2 +1/2 slope =-1/2. A perpendicular line has a negative inverse slope = +2

set (66-r^2)/15 = 2

66-r^2 = 30

r^2 = 36

r = 6 or -6