Question

The point on the curve `x^2=2y`which is nearest to the point (0, 5) is(A) `(2sqrt(2),4)` (B) `(2sqrt(2),0)` (C) (0, 0) (D) (2, 2)

Answer 1

If we see the options, option - `(B)` do not satisfy the equation of the curve.
So, it is not the answer.
Now, we will calculate the distance of rest of three options from `(0,5)`.
For Option - (A),
`d = sqrt((2sqrt2-0)^2+(4-5)^2) = 3`
For Option - (C),
`d = sqrt((0-0)^2+(0-5)^2) = 5`
For Option - (D),
`d = sqrt((2-0)^2+(2-5)^2) = sqrt13`
As, `d` in case of option - (A) is the minimum, so `(2sqrt2,4)` is the nearest point.