1. The coordinate of the point on y^2=8x which is closest from x^2 + (y+6)^2 =1 is ?

Ans:
Hello Student,
Please find answer to your question below

Minimum distance b/w any two curves lie along common normal
So if we find the coordinate where common normal touches the parabola, then thats coordinate will be closest to circle


Equation normal to parabola:

where m is slope of normal

So this common normal will pass through the centre of circle also
Centre (0, -6)
So,


m = 1 is one solution which is also clear from the figure.

Put this in parabola


y = -4, 12
x = 2, 18
(2, -4) is the closest which is clear from the diagram.