Have you ever learned the distance formula from a point to a straight line in junior high school mathematics?

Solution: Solve the equation-1/6x 2+ 1/6x+5 to get a (-5,0) and B (6 6,0).

Y =- 1/6 x 2+ 1/6 x+5。 The y axis is located at c (0 0,5) and the symmetry axis is X=0.5.

△APC's heart is on the coordinate axis, that is, it may be on the X axis or the Y axis.

Let the center of △APC be O, and when the center intersects the Y axis, ∠ ACO = ∠ PCO = 45.

∠ACP = 90°

The analytical formula of straight line CP is Y=-X+5.

The coordinate of the intersection of X=0.5 is P(0.5, 4.5).

∠ Cao =∠ Pao = 45, when the inner heart intersects with the X axis ∠ Cap = 90.

The analytical formula of linear AP is Y=-X-5.

The coordinate of the intersection of X=0.5 is P(0.5, -5.5).

A: The coordinates of point P are (0.5, 4.5), (0.5, -5.5).

This problem does not need the distance formula from point to straight line.

The formula of the distance from a point to a straight line was learned in high school.