From the figure shown here, we have OV = √2 and OS = 2√2. The vertex V is obtained as follows: (V(OV)cos45°, (OV)sin 45°) = (√2
1
√2
,√2
1
√2
) = (1 , 1) S = ((OS)cos45°, (OS)sin45°) S = (2, 2)
The equation of directrix is OV = VS where OV = √2 VS = √(2−1)2+(2−1)2 = √2 Now , a = √2 and therefore, x + y = 0 (directrix) Equation of parabola: we have P(x, y) and PS = PM √(x−2)2+(y−2)2 =