Question
The radius of the largest circle, which passes through the focus of the parabola y2=4(x+y) and contained in it is ???
Joshi sir comment
given equation can be written as (y-2)2= 4(x+1) so coordinate of focus (a, 0) will be x+1 = 1 and y - 2 = 0 so x = 0 and y = 2
let the centre of largest circle inside parabola is (k, 2) so equation of that circle will be (x-k)2 + (y-2)2 = k2
on solving parabola and circle we get x2 + (4-2k) x + 4 = 0
for largest circle roots of this quadratic equation should be equal so b2= 4ac
solve and get k = 4 so radius will be 4