Question

) Determine the equation of the straight lines through (1,-4) that makes an angle of 45 degree with straight line 2x +3y+7 =0​

Answer 1

Answer:

Step-by-step explanation:

2x−y+7=0

⇒y=2x+7

∴ Slope of the required line m  

1

​  

=2

⇒tan45=  

1+m  

1

​  

m

±m  

1

​  

−m

​  

=  

1+2m

±2−m

​  

 

⇒1=±  

1+2m

2−m

​  

 

Take positive sign 1+2m=2−m

⇒3m=1

∴m=  

3

1

​  

 

Take negative sign 1+2m=−2+m

⇒m=−3

Equation of the straight line passing through point (4,5) and its slope =m is y−5=m(x−4)

when m=  

3

1

​  

 equation of straight line  

⇒y−5=  

3

1

​  

(x−4)

⇒3y−15=x−4

⇒x−3y+11=0

and when m=−3  y−5=−3(x−4)

⇒3x+y−17=0

Hence, solved.