The gradient function of a curve is where is constant.The equation of the normal to the curve at point is ..
a)Find the value of
b)the equation of the curve.
The normal is
.
Therefore, the gradient of the tangent will be , since the tangent and normal are perpendicular.
So the gradient function at the point has a value of .
Substituting into the derivative gives
.
Now that you know , you know
.
Since lies on this curve
.
Thus the equation of the curve is .