1. Tardigrade
  2. Question
  3. Mathematics
  4. Let P a point on y2=4x such that its focal distance is 4. Let T be the point of intersection of tangents drawn at P and vertex of the parabola. If S is focus and 'R' is an interior point on the axis of the parabola at a distance 4 unit from S, then area of quadrilateral PRST is equal to

Q. Let $P$ a point on $y^{2}=4x$ such that its focal distance is $4.$ Let $T$ be the point of intersection of tangents drawn at $P$ and vertex of the parabola. If $S$ is focus and $'R'$ is an interior point on the axis of the parabola at a distance $4$ unit from $S,$ then area of quadrilateral $PRST$ is equal to

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Solution:

$P\left(a t^{2} , \, 2 a t\right)=P\left(t^{2} , \, 2 t\right)$
$⇒4=1+t^{2}⇒t^{2}=3$
  • ​​​​​​​ Solution
$T\left(\right.0, \, \sqrt{3}\left.\right), \, S\left(\right.1, \, 0\left.\right), \, P\left(\right.3, \, 2\sqrt{3}\left.\right), \, R\left(\right.5, \, 0\left.\right)$
Required area $=6\sqrt{3}$

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