Question

If the angle between the lines 2x+3y-5=0; 5x+ky-6=0 is π/4 then find the value of k.​

Answer 1

We know that, if y=mx+c is the equation of an straight line, then m is called the slope of the equation.

For the straight line,

4x−y+7=0

⟹y=4x+7

Therefore, m1=4 is the slope of the above equation.

Similarly, for the straight line,

kx−5y−7=0

⟹y=5kx+59

Therefore, m2=5k is the slope of the above equation.

The angle two two straight lines is given as:

tanθ=∣∣∣∣∣1+m1m2m1−m2∣∣∣∣∣

Therefore, the angle between the given straight lines is given as

tan450=∣∣∣∣∣∣∣∣1+4×5k4−5k∣∣∣∣∣