Find the coordinates of the points of intersection of the straight lines whose equations are
$y = m_{1} x + \frac{a}{m_{1}}$ and $y = m_{2} x + \frac{a}{m_{2}}$ .

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Solution

$y = m_{1} x + \frac{a}{m_{1}} . . . . . . (i) y = m_{2} x + \frac{a}{m_{2}}$

Substituting $y$ from $(i)$ , we get

$m_{2} x + \frac{a}{m_{2}} = m_{1} x + \frac{a}{m_{1}} (m_{2} - m_{1}) x = a (\frac{1}{m_{1}} - \frac{1}{m_{2}}) (m_{2} - m_{1}) x = a (\frac{m_{2} - m_{1}}{m_{1} m_{2}}) \Rightarrow x = \frac{a}{m_{1} m_{2}} y = m_{2} (\frac{a}{m_{1} m_{2}}) + \frac{a}{m_{2}} y = a (\frac{1}{m_{1}} + \frac{1}{m_{2}})$

So the point of intersection is $(\frac{a}{m_{1} m_{2}}, a (\frac{1}{m_{1}} + \frac{1}{m_{2}}))$

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Similar questions

y = m_{1} x + \frac{a}{m_{1}}

y = m_{2} x + \frac{a}{m_{2}}

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