calculus

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Ola, I'm not understanding this question, any assistance? Thank you very much.

Find the distance of the line y = 2x + 6 from the circle x^2 + y^2 = 0.5 Find
the point of the line that is closest to the circle.
[Hint: a point on the line is closest to the circle if it is closest to the centre of the circle.]

The distance is ______________

  • calculus -

    the line has slope 2.

    So, a perpendicular to the line will have slope -1/2, which will be the slope of the radius.

    A line through (0,0) with slope -1/2 is y = -1/2 x.

    This line intersects the circle at (-2/√10 , 1/√10). Now just find the distance between that point and the line.

    You can also follow the hint and minimize the distance formula directly.

  • calculus -

    Thank you very much, Steve.

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