Find points on line which are at 1 unit distance
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Step-by-step explanation:
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
(i.e) |t+2|=5
(i.e) t+2=±5
∴t=−7ort=3
Hence the required points are (-7,11) or ( 3,1)
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