Question 4 What are the points on the y-axis whose distance from the line x/3 + y/4 =1 is 4 units.
Class X1 - Maths -Straight Lines Page 233
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Let any point on the y-axis is (0,r)
Here, equation of line is x/3+y/4=1
4x + 3y = 12
A/C to question ,
distance of equation 4x +3y = 12 from (0,r) is 4 unit .
use the formula,
The distance from point (x1,y1) to the line ax + by + c is |ax+by+c|/√(a²+b²)
So,
|4×0+3×r-12|/√(4²+3²)=4
|3r -12|/5 = 4
|3r -12| = 20
now, break modulus we get
(3r - 12) = ±20
3r = 12±20 = 32, -8
r = 32/3 , -8/3
Hence, points on the y-axis are (0,-8/3) and (0,32/3)
Here, equation of line is x/3+y/4=1
4x + 3y = 12
A/C to question ,
distance of equation 4x +3y = 12 from (0,r) is 4 unit .
use the formula,
The distance from point (x1,y1) to the line ax + by + c is |ax+by+c|/√(a²+b²)
So,
|4×0+3×r-12|/√(4²+3²)=4
|3r -12|/5 = 4
|3r -12| = 20
now, break modulus we get
(3r - 12) = ±20
3r = 12±20 = 32, -8
r = 32/3 , -8/3
Hence, points on the y-axis are (0,-8/3) and (0,32/3)
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