TS EAMCET · Maths · Parabola
Let \(M\) be the foot of the perpendicular from a point \(P\) on the parabola \(y^2=8(x-3)\) onto its directrix and let \(S\) be the focus of the parabola. If \(\triangle S P M\) is an equilateral triangle, then \(P\) is equal to
- A \((4 \sqrt{3}, 8)\)
- B \((8,4 \sqrt{3})\)
- C \((9,4 \sqrt{3})\)
- D \((4 \sqrt{3}, 9)\)
Answer & Solution
Correct Answer
(C) \((9,4 \sqrt{3})\)
Step-by-step Solution
Detailed explanation
Given, that the \(\triangle S P M\) (which is shown in figure) is equilateral. Also, given parabola is \(y^2=8(x-3)\) focus of this parabola is \(S(5,0)\) and vertex \(A(3,0)\). Let coordinate of \(P\left(h+a t^2, k+2 a t\right)\) \(=P\left(3+2 t^2, 4 t\right)\) Then, coordinate…
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