Answer:
y = -
(x - 1)² + 2
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
= | y - 6 |
Square both sides
(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )
(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )
(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )
(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )
16y = - (x - 1)² + 32 ( divide all terms by 16 )
y = -
(x - 1)² + 2
The solution is (1,3). This is where the two lines intersect.
4/2 because 4/2=2 that is an integer
slope intercept form is: y = mx + b
m = slope
b = y-intercept
In the equation y = 1/4x + 8
m = 1/4 = slope
b = 8 = y-intercept