Under a force that varies inversely as the square of the distance from an attracting object (such as the sun exerts on Earth), it can be shown that the equation of the path an object follows is given in general by 1/r = a + b cos θ where a and b are constants for a particular path. First, transform this equation into rectangular coordinates. Then write one or two paragraphs explaining why this equation represents one of the conic sections, depending on the values of a and b. It is through this kind of analysis that we know the paths of the planets and comets are conic sections.