Question

About what point on parabola y=x^2 is 5 units away from the origin along the curve

Answer 1

the distance from the origin is 5, so

sqrt(x²+y²)=5

x²+y²=25

substitue y=x²

y+y²=25

y²+y-25=0

solve using calculator or the formula

to get

y =( -1+sqrt(1+4*25))/2

or y = (-1-sqrt(1+4*25))/2

the second solution is rejected because a square cannot be negative

the value of x is the positive or negative (sqrt... or -sqrt...) or y