EAMCET Engineering 2010 Solved Paper

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)