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If the area of the triangle inscribed in the parabola
$y^{2} = 4 a x$ with one vertex at the vertex of the parabola
and other two vertices at the extremities of
a focal chord is $5 a^{2} / 2$ then the length of the focal
chord is

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25a/4

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Correct option is C

Let the vertices be O(0,0),Aat2,2atBat2,−2at then 12||0012t22at1at22at11=5a22⇒2t2−5t+2=0⇒ t=2 or 1/2so the vertices of a focal chord are(4a, 4a) and (a/4, – a) (Taking t = 2) and lengthof this focal chord is 25 a/4.

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If the area of the triangle inscribed in the parabola y2=4ax with one vertex at the vertex of the parabolaand other two vertices at the extremities ofa focal chord is 5a2/2then the length of the focalchord is

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Ready to Test Your Skills?

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If the area of the triangle inscribed in the parabola
$y^{2} = 4 a x$ with one vertex at the vertex of the parabola
and other two vertices at the extremities of
a focal chord is $5 a^{2} / 2$ then the length of the focal
chord is