Question

RS aggrawal class 11
Straight lines

Q)Find all the points on the line x + y = 4 that lie at a unit distance from the 4x + 3y = 10.​

Answer 1

Step 1 :

The coordinates of the arbitrary point on x+y=4 can be obtained by putting x=t (or y=t) and then obtaining y(or x) from the equation of the line, where t is a parameter.

Substituting x=t in x+y=4 we get

y=4−t

∴ The coordinates of an arbitrary point on the given line are P(t,4−t).

Let P(t,4−t) be the required point.

Step 2 :

It is given that the distance of P from the line 4x+3y−10=0 is unity.

∴4t+3(4−t)−1042+32−−−−−√1=1

|t+2|=5

t+2=±5

∴t=−7

Hence the required points are (-7,11) or ( 3,1)