If the point P (2, - 1) is known, the equation of the line L which passes through the point P and has the largest distance from the origin is obtained, and the maximum distance is obtained;

If the point P (2, - 1) is known, the equation of the line L which passes through the point P and has the largest distance from the origin is obtained, and the maximum distance is obtained;

When the distance from the origin is the maximum, the distance from the origin to the straight line is exactly the distance between the origin and P, that is, the distance between the line segment OP is the maximum distance! The linear equation is very easy to find, because the slope of the straight line is perpendicular to op, so it's OK to write the equation directly in oblique form!