Question

8. Find the equations of the striaght lines passing through (1, 1) and which are at a
distance of 3 unit from (-2,3).​

Answer 1

Answer:

Suppose that the equation of line is

x+by+c=0.......(1)

The line passes through points (1,1)

Then,

1+b+c=0

⇒c=−(b+1)

The equation of the line is x+by−(b−1)=0.

The line is at a distance of 3 units from

(−2,3).

Now,

∣

∣

∣

∣

∣

1+b

2

−2+3b−(b+1)

∣

∣

∣

∣

∣

=3

⇒

∣

∣

∣

∣

∣

1+b

2

=3

2b−3

∣

∣

∣

∣

∣

On squaring both side and we get,

⇒

1+b

2

4b

2

−12b+9

=9

⇒4b

2

−12b+9=9+9b

2

⇒5b

2

+12b=0

⇒b(5b+12)=0

⇒b=0,5b+12=0

⇒b=0,b=−

5

12

Hence, the equation of ,line is x+by−(b+1)=0

If b=0 then,

Equation of line is x−1=0

If b=−

5

12

Then equation of line is

x−(

5

12

)+

5

7

=0

5x−12y+7=0

Hence, this is the answer.