Question

9. Let (x, y) be a point lying on the graph of y=√x. Let d denote the distance from (x, y) to the point (1,0). Find a formula for d^2 that depends only on x.

10. Using your answer to Problem 9, find the point (x₀, y₀) on the graph ofy=√x that has the smallest possible distance to (1,0).

Answer 1

(9)

We can find distance between (x,y) and (1,0)

we are given

we can plug it

we can square both sides

..........Answer

(10)

we can find derivative

we can plug d'=0

and then solve for x

now, we can find y

so, we get point as

..............Answer