Question

find the acute angle between the lines 3x-4y=420 and 4x+3y=420​

Answer 1

३x-४y=420and 4x+3y=420

Answer 2

Given,

Two lines are given with equations, 3x-4y=420 and 4x+3y=420​ respectively.

To find,

The angle between the two lines.

Solution,

The angles between two lines can be given by,

tan Ф= ( m2 - m1 )/( 1 + m1 m2 ),

where, tan Ф is the angle between two lines and m1, m2 is the slope of the given two lines.

Slope (m1) of 3x-4y=420:

⇒   3x - 4y= 420.

⇒   -4y = -3x + 420.

⇒   y = (-3/-4) x + (-420/4)

Hence, slope m1 = 3/4.

Similarly, Slope (m2) of 4x +3y=420:

⇒   4x +3y=420

⇒   3y = -4x +420

⇒   y = (-4/3)x + (420/4)

Hence, slope m2 = -4/3.

Thus, the angle between two lines

⇒   tan Ф  =   $\frac{(3/4)-(-4/3)}{1+(3/4)(-4/3)}$

⇒   tan Ф  =   $\frac{(3/4 + 4/3)}{0}$

⇒   tan Ф  = undefined.

tan Ф  is undefined at 90°.

Hence, angles between the two lines 3x-4y=420 and 4x+3y=420​  are 90°.