If the lines 2y = x + 3 and y = 3x + 1 are equally inclined to the line, y = mx + 4, then the value of m is

Question

If the lines 2y = x + 3 and y = 3x + 1 are equally inclined to the line, y = mx + 4, then the value of m is (A) (1±5√2/7) (B) (5√2-1/7) (C) (1-5√2/5) (D) None of these

Tardigrade Admin · Accepted Answer

We have, (m-m1/1+m1m)=(m2-m/1+mm2) ⇒ (m-3/1+3m)=-((2m-1)/m+2) ⇒ (m - 3) (m + 2) + (2m - 1) (1 + 3m) = 0 ⇒ 7m2-2m-7=0 ⇒ m=(1±5√2/7)

Q. If the lines $2 y = x + 3$ and $y = 3 x + 1$ are equally inclined to the line, $y = m x + 4$ , then the value of $m$ is

$\frac{1 \pm 5 2}{7}$

$\frac{5 2 - 1}{7}$

$\frac{1 - 5 2}{5}$

None of these

We have,
$\frac{m - m _{1}}{1 + m _{1} m} = \frac{m _{2} - m}{1 + m m _{2}}$
$\Rightarrow \frac{m - 3}{1 + 3 m} = - \frac{( 2 m - 1 )}{m + 2}$
$\Rightarrow (m - 3) (m + 2) + (2 m - 1) (1 + 3 m) = 0$
$\Rightarrow 7 m^{2} - 2 m - 7 = 0$
$\Rightarrow m = \frac{1 \pm 5 2}{7}$

Q. If the lines 2y=x+3 and y=3x+1 are equally inclined to the line, y=mx+4, then the value of m is

71±52​​

752​−1​

51−52​​