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What are the points on y-axis which are at a distance of 4 units from 4x+3y=12

User Trallnag
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1 Answer

5 votes

Given:

The equation of line is


4x+3y=12

To find:

The points on y-axis which are at a distance of 4 units from the given line.

Solution:

The point lie on the y-axis. So, their x-coordinate must be zero.

Let the points are in the form of (0,k).

The distance between a point
(x_0,y_0) and a line
ax+by+c=0 is


d=(|ax_0+by_0+c|)/(√(a^2+b^2))

The given equation can be written as


4x+3y-12=0

The distance between (0,k) and
4x+3y-12=0 is 4 units.


4=(|4(0)+3(k)-12|)/(√(4^2+3^2))


4=(|0+3k-12|)/(√(16+9))


4=(|3k-12|)/(√(25))


4=(|3k-12|)/(5)

Multiply both sides by 5.


20=|3k-12|


\pm 20=3k-12


12\pm 20=3k


(12\pm 20)/(3)=k

Now,


k=(12-20)/(3)\text{ and }k=(12+20)/(3)


k=(-8)/(3)\text{ and }k=(32)/(3)

Therefore, the two points are
\left(0,(-8)/(3)\right)\text{ and }\left(0,(32)/(3)\right).

User Scottmf
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6.3k points