math

Calculus There is a famous' family of curves called conchoids. There are various ways to describe a conchoid, including a polar equation, a cartesian equation and a geometric construction. The particular example be- low was first studied by the Greek mathematician Nicomedes around 200BC. Let's look at the cartesian equation of a conchoid of Nicomedes. It is given by (x - 1)2(22 + ?) = 22. Here is a picture of this conchoid -2 -1 1 3 4 -2 (a) Use implicit differentiation to find dy dx as a function of r and y. (b) Find the slope of the tangent to the curve at the point where r= ; and y > 0