Given curves are
y2 = 4x and x2 + (y + 12)2 = 1
Since both the tangents at P and Q are parallel.
So their slopes are same.
when y = 4, then x = 4
So the point Q is (4, 4)
Here, C = (0, – 12)
Thus, Shortest distance
= PQ
= CQ – CP
= √(16 + 64) – 1
= √80 – 1
= 2√5 – 1