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.
Answers
Answered by
27
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)
Similar questions