The parametric of the a parabola is given by x = ø + 1 and y = ø^2 + 2ø + 2 what is the equation of the normal to the parabola at the point (-1,0)

Answer 1

x = t + 1 = -1

t = -2

The difference quotient gives y' = 2*t + 2

The slope of the normal line is then 2(-2) +2 = -4 + 2 = -2

SO the normal line has slope -2 and eats (-1,0)

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

y = -2x - 2