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Question

Question: If the lines \(m\)=...

If the lines mm=

A

1+327\frac { 1 + 3 \sqrt { 2 } } { 7 }

B

1−327\frac { 1 - 3 \sqrt { 2 } } { 7 }

C

1+327\frac { 1 + 3 \sqrt { 2 } } { 7 }

D

1±527\frac { 1 \pm 5 \sqrt { 2 } } { 7 }

Answer

1±527\frac { 1 \pm 5 \sqrt { 2 } } { 7 }

Explanation

Solution

If line y=mx+4y = m x + 4 are equally inclined to lines with slope m1=3m _ { 1 } = 3 and m2=12m _ { 2 } = \frac { 1 } { 2 } ,then (3−m1+3m)=−(12−31+12m)\left( \frac { 3 - m } { 1 + 3 m } \right) = - \left( \frac { \frac { 1 } { 2 } - 3 } { 1 + \frac { 1 } { 2 } m } \right)

⇒ m=1±527m = \frac { 1 \pm 5 \sqrt { 2 } } { 7 }