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Question

The radius of the largest circle, which passes through the focus of the parabola y2=4(x+y) and also contained in it, is 


Solution


y2=4(x+y)
(y2)2=4(x+1)     ...(1)
Its focus is (0,2).
Let radius of the circle be r.
Then, equation of circle is
(xr)2+(y2)2=r2     ...(2)
Solving eqns. (1) and (2), we get
(xr)2+4(x+1)=r2
x2+(42r)x+4=0
(42r)216=0     [D=0]
42r=±4
r=4

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