Shortest Distance between Two Curves

Q. If $P$ is a point on the parabola $y=x^2+4$ which is closest to the straight line $y=4x-1,$ then the co-ordinates of $P$ are

1. $(-2,8)$
2. $(1,5)$
3. $(3,13)$
4. $(2,8)$

Q. Find the shortest distance between the line $x-y+1=0$ and the curve $y^2=x$.

Q.

C1 and C2 are two non-intersecting curves. Common normal of C1 and C2 intersect at the points (1, 0) and (4, 4) on the curves. If the slope of the normal is 30 degrees, find the shortest distance between the curves assuming they have only one common normal

1. 5

2. 
   $5\tan \left(30°\right)$

3. $5\sin \left(30°\right)$

4. $5\cos \left(30°\right)$