Question

If points (a, 0), (0, b) and (x, y) are collinear, then will hold true.

• A. $\frac{x}{a}+\frac{y}{b}=1$
• B. $\frac{x}{a}-\frac{y}{b}=1$
• C. $\frac{y}{a}+\frac{x}{b}=1$
• D. $\frac{y}{a}-\frac{x}{b}=1$

Answer 1

The correct option is A $\frac{x}{a}+\frac{y}{b}=1$

Let A(a, 0), B(0, b) and P(x, y) be the collinear points.
$\Rightarrow \mathrm{Slope}\mathrm{of}\mathrm{AB}=\mathrm{Slope}\mathrm{of}\mathrm{BP}\Rightarrow \frac{b-0}{0-\left(-a\right)}=\frac{y-b}{x-0}\Rightarrow \frac{-b}{a}=\frac{y-b}{x}\Rightarrow -\mathrm{xb}=\mathrm{ay}-\mathrm{ab}\Rightarrow \mathrm{xb}+\mathrm{ay}=\mathrm{ab}\Rightarrow \frac{x}{a}+\frac{y}{b}=1$