Find the equation of the normal to the curve at , where .
First, find the slope function by differentiating with respect to .
To find the slope when , substitute this value into the slope function.
Therefore, the slope of the tangent at the point where is 2, and hence the slope of the normal to the curve at this point
is (the negative reciprocal of 2).
Now find the -coordinate when by substituting into the equation of the curve.
Therefore the normal to the curve has a slope of and passes through the point .
Its equation can be found using the general equation of a straight line.
Making the substitution gives