Equation of line in Straight lines

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A line with positive rational slope passes through the point A(6, 0) and is at a distance of 5 units from B(1, 3). If the slope of the line is m, then the value of 75m is

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Solution

Equation of line passing through point A(6, 0) and having slope m is $(y - 0) = m (x - 6), m > 0$
$or m x - y - 6 m = 0, m > 0 - - - - - - (1)$
Distance of this line from point B(1,3) is 5.
$\begin{array}{l} So, |\frac{m - 3 - 6 m}{\sqrt{1 + m^{2}}}| = 5 \\ \Rightarrow (3 + 5 m)^{2} = 25 (1 + m^{2}) \\ \Rightarrow 9 + 30 m = 25 \\ \Rightarrow m = \frac{16}{30} = \frac{8}{15} \end{array}$

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

A line with positive rational slope passes through the point A(6, 0) and is at a distance of 5 units from B(1, 3). If the slope of the line is m, then the value of 75m is

Equation of line passing through point A(6, 0) and having slope m is (y−0)=m(x−6),m>0 or mx−y−6m=0,m>0------(1)Distance of this line from point B(1,3) is 5. So, m−3−6m1+m2=5⇒ (3+5m)2=251+m2⇒ 9+30m=25⇒ m=1630=815

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