Analytic Geometry

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Find the equation of the circle with radius sqrt2 tangent to the line x+y=3 and having its center on the line y=4x

  • Analytic Geometry -

    let the centre be (a,b)
    but (a,b) lies on y = 4x
    so b = 4a
    and we can call our centre (a, 4a)
    so the equation of our circle is

    (x-a)^2 + (y-4a)^2 = 2

    we know the distance from (a,4a) to
    x+y-3 = 0 is √2

    |a + 4a - 3|/√(1+1) = √2
    5a - 3 = 2
    5a = 5
    a = 1

    so the circle equation is
    (x-1)^2 + (y-4)^2 = 2

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