Question

Find the equations of the lines which pass through (4, 5) and make equal angles with
the lines 5x – 12y + 6 = 0 and 3x = 4y + 7.
​

Answer 1

Step-by-step explanation:

Let the Slope of line be m

Now, slope of other lines are

4

3

,

5

12

The Slope is Equally inclined so it must lie between these slopes

such that

4

3

<m<

5

12

As it is equally inclined so angle between the line and the two given line must be same

⇒θ

1

=θ

2

⇒tanθ

1

=tanθ

2

⇒

1+

5

12

m

5

12

−m

=

1+

4

3

m

m−

4

3

⇒63m

2

−32m−63=0

⇒m=

2∗63

32±

32

2

+4∗63∗63

⇒m=

9

−7

,

7

9

Now, Equation of line as it passes through (4,5) will be

y−5=m(x−4)

Putting the obtained values of m in above Equation we get

9x−7y=1

7x+9y=73