An isosceles triangle has its vertex at the origin and its base parallel to the [math]x[/math]-axis with the vertices above the axis on the curve [math]y=27-x^2[/math]. [br][br]Drag [color=#1e84cc][b]point [i]P[/i][/b][/color] along this parabola. Find the coordinate of [math]P[/math] that maximize the area of the isosceles triangle. What is the maximum area this triangle can have?

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]