Take a point on the Y axis so that the distance from it to the curve MN is always greater than or equal to the square root of 6, and the ordinate of this point is between 5 and 8.

Is it necessary to set up a circle, state at the same time, and seek the supplement of delta problem?

Find the minimum value of the origin

Solution: Let a point on the Y axis be P(0, y).

And the ordinate of this point is between 5 and 8.

And then 5.

From points m (2 2,4) and n (3 3,9)

The equation of the straight line MN is:

5x-y-6=0。

The distance from point P to line MN is |y+6|/√26.

By taking a point on the Y axis, the distance from it to the curve MN is always greater than or equal to the square root of 6.

Get (|y+6|/√26)≥√6.

That is |y+6|≥2√39,

Get y+6≤-2√39.

Or y+6≥2√39.

That is, y≤-6-2√39 (give up, ∫5

Or y≥-6+2√39.

The minimum value to the origin is: -6+2√39.