Find the values of k for which the length of the perpendicular from the point (4, 1) on the line 3x - 4y + k = 0 is 2 units ?

Question

Question

Answer 1

CONCEPT:

The perpendicular distance d from P (x1, y1) to the line ax + by + c = 0 is given by

CALCULATION:

Given :The length of the perpendicular from the point (4, 1) on the line 3x - 4y + k = 0 is 2 units.

Let P = (4, 1)

Here x₁ = 4, y₁ = 1, a = 3, b = - 4 and d = 2

Now substitute x1 = 4 and y1 = 1 in the equation 3x - 4y + k = 0

⇒ |3⋅ x1 - 4 ⋅ y1 + k| = |12 - 4 + k| = |8 + k|

⇒

As we know that, the perpendicular distance d from P (x1, y1) to the line ax + by + c = 0 is given by

⇒

⇒ |8 + k| = 10

⇒ k = 2 or - 18

Hence, option C is the correct answer.