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 ______________
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.
Thank you very much, Steve.