what would the c and y coordinates be

Question

y = sqrt(x) such that the line through P and (1, 1) has slope 2/3 .

what would the c and y coordinates be?

Answer 1

y= sqrx

y' = 1/2sqrx = slope = 2/3

(y-1)/(x-1) = 2/3

(y-1)/(y^2 -1) = 2/3 cross multiply

2y^2 -2 = 3y- 3

2y^2 -3y + 1 = 0

factor

(2y-1)(y-1) = 0

y = 1/2 or 1

x = 1/4 or 1

(1,1) is a point on the parabola, so is point P (1/4, 1/2)

Point P has x=1/4 and y=1/2