Question

if (a,0) (b,0) (1,1) are these three points in a line than find the value of 1/a + 1/b = ?​

Answer 1

$\textbf{Given points are}$

$(a,0),\;(0,b)\;\text{and}\;(1,1)$

$\text{First we find the equation of the line joining (a,0) and (0,b)}$

$\text{The equation of the line joining (a,0) and (0,b) is}$

$\displaystyle\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}$

$\displaystyle\frac{y-0}{b-0}=\frac{x-a}{0-a}$

 

$\displaystyle\frac{y}{b}=\frac{x-a}{-a}$

$\displaystyle\;-ay=bx-ab$

$\implies\displaystyle\bf\;bx+ay=ab$

$\text{Since the points (a,0) (0,b) (1,1) are collinear,}$

$\text{(1,1) will lie on the line bx+ay=ab }$

$\implies\,b(1)+a(1)=ab$

$\implies\,b+a=ab$

$\text{Divide both sides by ab, we get}$

$\frac{b}{ab}+\frac{a}{ab}=\frac{ab}{ab}$

$\implies\bf\frac{1}{a}+\frac{1}{b}=1$

$\therefore\textbf{The value of \bf\frac{1}{a}+\frac{1}{b} is 1}$

Find more:

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