<span>Answer:
Its too long to write here, so I will just state what I did.
I let P=(2ap,ap^2) and Q=(2aq,aq^2)
But x-coordinates of P and Q differ by (2a)
So P=(2ap,ap^2) BUT Q=(2ap - 2a, aq^2)
So Q=(2a(p-1), aq^2)
which means, 2aq = 2a(p-1)
therefore, q=p-1
then I subbed that value of q in aq^2
so Q=(2a(p-1), a(p-1)^2)
and P=(2ap,ap^2)
Using these two values, I found the midpoint which was:
M=( a(2p-1), [a(2p^2 - 2p + 1)]/2 )
then x = a(2p-1)
rearranging to make p the subject
p= (x+a)/2a</span>
The equation of the line in standard form is x + 4y = 8
<h3>How to determine the line equation?</h3>
From the question, the points are given as
(0, 2) and (8, 0)
To start with, we must calculate the slope of the line
This is calculated using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 2) and (8, 0)
Substitute the known parameters in Slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
Slope = (0 - 2)/(8 - 0)
Evaluate
Slope = -1/4
The equation of the line can be calculated using as
y - y₁ = m(x + x₁)
Where
(x₁, y₁) = (0, 2)
and
m = slope = -1/4
Substitute the known values in the above equation
So, we have the following equation
y - 2 = -1/4(x - 0)
This gives
y - 2 = -1/4x
Rewrite as
1/4x + y = 2
Multiply by 4
x + 4y = 8
Hence, the line has an equation of x + 4y = 8
Read more about linear equations at
brainly.com/question/4074386
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