Question

To fit the straight line y=mx+c to n observations the normal equations are

Answer 1

Answer:

Let the given line y = mx + c be a normal line to the parabola y^2 = 4ax at the point P(at^2, 2at) . Then the slope of the tangent m´ at the point P and the slope of the normal line m must satisfy the condition (m·m´) = -1 .But m´ = (dy/dx)p = (1/t) ==> m = - t . Since the normal line passes through the point P, Therefore , we nave ;

2at = (-t)(at^2) + c ==> c = 2at + at^3 = 2a(-m) + a(-m)^3 = -2am - ma^3 and this is the required condition . And normal line is y = mx - 2am - ma^3 at the point P(at^2, 2at) or P(am^2 , -2am).