Q.

The radius of the circle touching the parabola y2 = x at (1, 1) and having the directrix of y2 = x as its normal is

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a

554

b

558

c

1053

d

None of these

answer is C.

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Detailed Solution

The equation of normal at P(1, 1) is y−1=−2(x−1) or y+2x=3 ...(i)
The directrix of the parabola y2=x is x=14 ...(ii)
The center of the circle is the intersection of two normals to the circle, i.e., (i) and (ii).
Therefore, the center is 14,72.
Hence, the radius of the circle is 1+142+1722=2516+254=554

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