Question

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

Answer 1

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.