find the value of k if the line 2x-y+k=0 may touch the circle x^2 + y^2=5​

Question

find the value of k if the line 2x-y+k=0 may touch the circle x^2 + y^2=5​

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Ladonna 4 years 2021-08-15T23:56:21+00:00 1 Answers 227 views 0

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  1. giabao
    0
    2021-08-15T23:57:58+00:00
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    Answer:

    k = ±4

    Step-by-step explanation:

    Equation of the circle is:

    x² + y² = 5​

    This means from the general form of equation of a circle;

    Centre coordinates is (0, 0) and radius is; √5.

    The line 2x – y + k = 0 touches the circle. Thus, perpendicular distance from centre of the circle to this line is equal to the circle radius;

    Thus;

    |((2 – 0) – (1 × 0) + k)|/(√(2² + 1²)) = √5

    |(1 + k)|/√5 = √5

    Multiply both sides by √5 to get;

    |1 + k| = 5

    |k| = 5 – 1

    k = ±4

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