Q. 44.0( 33 Votes )

# What are the points on the y-axis whose distance from the line is 4 units.

Answer :

The given line can be written as 4x + 3y -12 = 0

On comparing equation (1) to the general equation of line Ax + By + C = 0, we get,

A = 4 , B = 3 and C = -12.

It is known that the perpendicular distance (d) of the line Ax + By + C = 0 from a point

(x_{1}, y_{1}) is given by

Therefore, if (0,b) is the point on the y – axis whose distance from line is 4 units, then,

⇒ 20 = |3b – 12|

⇒ 20 = (3b – 12)

⇒ 20 = (3b – 12) or 20 = -(3b-12)

⇒ 3b = 20 +12 or 3b = -20 +12

⇒

Therefore, the required points are

Rate this question :

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

RS Aggarwal - MathematicsThe distance between the orthocenter and circumcentre of the triangle with vertices (1, 2) (2, 1) and is

RD Sharma - MathematicsWhat are the points on the x-axis whose perpendicular distance from the line is 4 units?

RS Aggarwal - MathematicsFind the equation of a line for which

p = 8, α = 225°

RD Sharma - MathematicsFind the equation of a line for which

p = 4, α = 150°

RD Sharma - MathematicsArea of the triangle formed by the points ((a + 3)(a + 4), a + 3), ((a + 2)(a + 3), (a + 2)) and ((a + 1)(a + 2), (a + 1)) is

RD Sharma - MathematicsFind the equation of straight line passing through ( – 2, – 7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.

RD Sharma - MathematicsFind the distance of the line 2x + y = 3 from the point ( – 1, – 3) in the direction of the line whose slope is 1.

RD Sharma - Mathematics