1.

A circle S having centre (alpha, beta) intersect at three points A, B and C such that normals at A,B and C are concurrent at (9,6) for parabola y^(2)=4x and O origin. Then,

Answer»

Sum of modulus of SLOPES of normals at points `A, B` and `C` is 6
`alpha+beta=4`
Magnitude of NORMAL having negative slope is 2
Circle `S` also passes through `O`

Solution :`:'y=mx-2m-m^(3)`
`implies6=9m-2m-m^(3)`
`impliesm^(3)-7m+6=0impliesm=1, +2, -3`
`:.` Centre is `(11/2, 3/2)`


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