If the tangents at point P & O on the parabola $y^{2} = 4 a x$ meet at the point T then the triangle $Δ S P T$ & $Δ S T Q$ (S is focus)

are similar

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are congruent

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have equal area

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have equal perimeter

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Solution

The correct option is A are similar
If tangent at point P and Q on parabola $y^{2} = 4 a x$ meet at point T then the $△ P S T$ and $△ Q S T$ (S is focus) is:
$T \equiv (a t_{1} t_{2}, a (t_{1} + t_{2})) S T = S T ∠ S P T = ∠ S Q T = 90^{0} Q T = P T$
So, condition side Angle side is fulfilled
$\Rightarrow △ S P T$ and $△ S Q T$ is similar.

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If the tangents at point P & O on the parabola y2=4ax meet at the point T then the triangle ΔSPT & ΔSTQ (S is focus)

The correct option is A are similarIf tangent at point P and Q on parabola y2=4ax meet at point T then the △PST and △QST (S is focus) is:T≡(at1t2,a(t1+t2))ST=ST∠SPT=∠SQT=900QT=PTSo, condition side Angle side is fulfilled ⇒△SPT and △SQT is similar.

If the tangents at point P & O on the parabola $y^{2} = 4 a x$ meet at the point T then the triangle $Δ S P T$ & $Δ S T Q$ (S is focus)