Given, that the △SPM (which is shown in figure) is equilateral. Also, given parabola is y2=8(x−3) focus of this parabola is S(5,0) and vertex A(3,0).
Let coordinate of P(h+at2,k+2at) =P(3+2t2,4t) Then, coordinate of M(−5,4t). We know that the side of this equilateral triangle is 4a=4×2=8 Now, PS=8 √(3+2t2−5)2+(4t)2=8 ⇒√(2t2−2)2+(4t)2=8 ⇒√(2t2+2)2=8 ⇒2t2+2=8 ⇒2t2=6 ⇒t=√3 ∴P(3+2×3,4×√3)=P(9,4√3)