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Find the points on y-a xi s whose perpen...

Find the points on `y-a xi s` whose perpendicular distance from the line `4x-3y-12=0` is `3.`

Text Solution

Verified by Experts

The correct Answer is:
(0,1) and (0,9)
Let the required point be `P(0, alpha)`. It is given that the length of the perpendicular from `P(0, alpha)` on 4x-3y-12=0 is 3. Therefore,
`|(4(0)-3alpha-12)/(sqrt(4^(2)+(-3)^(2)))|=3`
`"or " |3alpha+12| = 15`
`"or " |alpha+4| = 5`
`"or " alpha+4 =+-5`
`"or " alpha = 1, -9`
Hence, the required points are (0,1) and (0,-9).
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Knowledge Check

  • The perpendicular distance from (1,2) to the line 5x+12y-3=0 is:

    A
    2
    B
    3
    C
    4
    D
    5

  • The points on the line x + y = 4 lying at a unit distance from the line 4x+3y-10=0 are

    A
    (-7, 11), (3, 1)
    B
    (7, -11), (3, -1)
    C
    (-7, 11), (-3, 7)
    D
    (7, -3), (21, -7)

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