# calculus

posted by Kevin Land

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 ______________

1. Steve

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.

2. Kevin Land

Thank you very much, Steve.

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