How do I find the equation of the normal to the curve y=x^2 at the point (x1,y1)? Where x1=2 and y1=4 .

I would get the student to draw a diagram of the situation.. so draw the curve y=x^2, the tangent at (2,4) and then the normal. Then I would highlight to them that the equation we want is the equation of a straight line.. with the form y=mx+c. Then we would need m and c. So, m first, let's use the fact that the tangent gradient multiplied by the normal gradient must be minus 1. So we can find the gradient of the tangent to the curve using differentiation, and then utilise that result to find m for the normal. Now we need c... so we know a point the curve passes through (2,4).. now all we need to do is to plug those x and y values that satisfy the equation we want to find and plug in the m value from before into the general equation y=mx+c. From which we can find c. So c and m have both been found. Hence we have found the equation we are looking for.