Find the equation for each of the followings items below:?

Question

Find the equation for each of the followings items below:

a. A line that passes through (1, 1) and is perpendicular to the line 3x+4Y=12.

b. A line that passes through (5,4) and has a slope of 2.

c. A line that passes through (9,8) and has a slope of -1.

d. A line that passes though the points (1,2) and (12,24)

e. A circle with a radius of 9 and a midpoint at (3,3)

Answer 1

a. 3x + 4y = 12
...4y = -3x + 12
...y = -3/4x +12
...the perpendicular has slope 4/3.
...use (1,1) to find y-intercept:
...1 = 1*4/3 + b
...b = 1-4/3 = -1/3
...ans. y = -4/3x - 1/3

b. 4 = 2*5 + b
...b = 4 - 10 = -6
...y = 2x - 6

c. 9 = -1*8 + b
...b = 9 + 8 = 17
...y = -x + 17

d. m = (24 - 2)/(12 - 1) = 22/11 = 2
...2 = 2*1 + b
...b = 0
...y = 2x

e. (x - 3) + (y - 3) = 81

Answer 2

gebobs made a slip


e. (x - 3) + (y - 3) = 81
should be

eqt of circle = (x-h)² + (y-k) ² = r²
=> (x - 3)² + (y - 3)² = 81