ABC is an isosceles triangle with its base BC twice its altitude. A point P moves within the triangle such that the square of its distance from BC is half the rectangle contained by its distances from the two sides. Show that the locus of P is an ellipse with eccentricity √2/3 passing through B & C.
B = (a, 0) C = (–a, 0) & A = (a, 0) Equation of line AB is
x + y = a and that of AC is y = x + a
Let P= (x, y) distance from BC = y
And area of PRAS = PR x PS
When it is +4y2 it forms a hyperbola.
When it is –4y2 it forms an ellipse
