Answer:
[tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]
Step-by-step 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
[tex]\frac{y - 2b}{2b - 0} = \frac{x - 2a}{2a - c}[/tex]
⇒ [tex]y - 2b = \frac{2b}{2a - c}x - \frac{4ab}{2a - c}[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x - \frac{4ab}{2a - c} + 2b[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x + \frac{-4ab + 4ab - 2bc}{2a - c}[/tex]
⇒ [tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]
Therefore, third option is correct. (Answer)
We know that the equation of a straight line passing through the points ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) is given by
[tex]\frac{y - y_{1} }{y_{1} - y_{2}} = \frac{x - x_{1} }{x_{1} - x_{2}}[/tex]
