Question

what's the equations of both lines through the point (2,3) that are tangent to the parabola y=x^2+x

Answer 1

y = x^2+x

dy/dx = 2x+1
dy/dx= m
m = 2x+1
At(2,3)
m = 2(2)+1
m = 5 slope of normal line -1/5
Point (2,3)
equation y-y1 = m (x-x1)
y-3 = 5(x-2) : y-3 = -1/5(x-2)
y-3 = 5x-10 : y-3 = -x/5+2/5
y = 5x-7 : y = -x/5+17/5
Equation of Tangent line y = 5x-7
Equation of Normal line y = -x/5+17/5