Question

the angle between the lines 2x+y+1=0 and x+ky+5=0 is 90 degree the k is​

Answer 1

Answer:

k=-2

Step-by-step explanation:

2x+y+1=0------------(1)

and x+ky+5=0---------(2)

The eqn of line (1) can be written as

y=-2x-1

thus slope m1=-2

The eqn of line (2) can be written as

ky=--x-5

y=-x/k-5/k

so slope m2=-1/k

If line(1) and (2 ) are perpendicular then

m1m2=-1

Or (-2)(-1/k)=-1

2/k=-1

-k=2

k=-2

Answer 2

$\sf \: Since \: the \: lines \: are \: \\ \sf perpendicular \: to \: eachother \: then$

$\sf \boxed{m_{1} \times m_{2} = ( - 1) }$

$\frac{ - 2}{1} \times \frac{ - 1}{k} = - 1 \\ 2 = - k \\ \boxed{ \sf \: k = ( - 2) }$

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