Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Answer-

(78,104) is the closest to the interior point.

Solution-

The equation of the circle,

As the point will be on the circle, so the coordinate of the point will be,

The distance "d' between the point and (30,40) is,

Now, we have to calculate x for which d is minimum. d will be minimum when    will be minimum.

Let,

Finding the critical values,

Then,

f''(x) is positive, so f(x) will be minimum at x=78

For x = 78, y will be

Therefore, the point is (78,104)

2

step-by-step explanation: