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JEE Main20249 Apr 2024Evening ShiftMathematicsParabolaActual

Consider the circle C: x^2+y^2=4 and the parabola P: y^2=8 x . If the set of all values of , for which three chords of the circle C on three distinct lines passing through the point ( , 0) are bisected by the parabola P is the interval (p, q) , then (2 q-p)^2 is equal to ________

Correct answer

0

Step-by-step solution

aligned & T=S₁ & x₁+y₁=x₁^2+y₁^2 & x₁=x₁^2+y₁^2 & (2 t^2 )=4 t^4+16 t^2 & =2 t^2+8 & -8 2 =t^2 aligned Also, 4 t ^4+16 t ^2-4 < 0 aligned & t ^2=-2+ 5 & =4+2 5 & (8,4+2 5 ) & (2 q - p )^2=80 aligned

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