Question

find the points on the line x-y-1=0 which are at diatance root2 units from (1,5)​

Answer 1

Step-by-step explanation:

Let the required points on the line x+y+1=0 be (h,k)

k=−1−h

Since the perpendicular distance of (h,k) from the line 3x+4y+2=0 is

5

1

,

3

2

+4

2

∣3h+4k+2∣

=

5

1

⇒

5

∣3h+4(−1−h)+2∣

=

5

1

⇒∣3h−4−4h+2∣=1

⇒∣−h−2∣=1

⇒−h−2=1or−h−2=−1

∴h=−3,−1 and correspondingly k=2,0

The required points are (−3,2) and (−1,0)