Question

Can someone show how to solve this problem

Find the equation of the line normal to the graph of y = x^2 + 1 that passes through the point (1, 2).

Thanks!

Answer 1

dy/dx = 2x
which is the slope of the tangent at any point (x,y) on the parabola
so at (1,2) , the slope of the tangent is 2(1) = 2
since the normal is perpendicular to the tangent, the slope of the normal must be -1/2

equation:
y-2 = (-1/2)(x-1)

you can doctor that up any way you need.