Question

The slope of line éb is zac

What is the equation of D. simplified?
B(2a, 2b)
y-yı = m(x - xı)
y-0=(220)(x-c)
y=[0]x-(22b)
y=(220 fer-(2 bezed
y=(22]x- (226)
O y=(,20 ]- (250)
Ela, b)
A(0, 0)
Dac, 0)
C(2c, 0)

Answer 1

`y = (2b)/(2a - c) x - (2bc)/(2a - c)`

Explanation:

The straight line BD passes through points B(2a,2b) and D(c,0).

Therefore, the equation of the straight line BD will be given by

`(y - 2b)/(2b - 0) = (x - 2a)/(2a - c)`

⇒
`y - 2b = (2b)/(2a - c)x - (4ab)/(2a - c)`

⇒
`y = (2b)/(2a - c) x - (4ab)/(2a - c) + 2b`

⇒
`y = (2b)/(2a - c) x + (-4ab + 4ab - 2bc)/(2a - c)`

⇒
`y = (2b)/(2a - c) x - (2bc)/(2a - c)`

Therefore, third option is correct. (Answer)

We know that the equation of a straight line passing through the points (
`x_(1),y_(1)`) and (
`x_(2),y_(2)`) is given by

`(y - y_(1) )/(y_(1) - y_(2)) = (x - x_(1) )/(x_(1) - x_(2))`