A point on the parabola whose focus is S(1,-1) and whose vertex is A(1,1) is

Step-by-step solution

(a) The gradient of the line joining the focus S(1,-1) and vertex A(1,1) is m= -1-1 1-1 =0 Let Q(h, k) be the point of intersection of the axis A S with the directrix. The A(1,1) will be the mid-point of Q S . array rlrl & & & h+1 2 & & 1 and k-1 2 =1 & & h & =1 and k=3 array Q is the point (1,3) So, the directrix passes through the point (1,3) and has the gradient 0 . The equation of the directrix is y-3=0 Let P(x, y) be any point on the parabola and M be the foot of the perpendicular drawn from P on the directrix