Question

(a) Graph the conics \({\rm{r = ed/(1 + esin\theta )}}\) for \({\rm{e = 1}}\)and various values of \({\rm{d}}\).How does the value of \({\rm{d}}\)affect the shape of the conic?

(b) Graph these conics for \({\rm{d = 1}}\)and various values of \({\rm{e}}\)How does the value of \({\rm{e}}\)affect the shape of the conic?

Short answer

\({\rm{e < 0}}\)the graph is ellipse and \({\rm{e > 0}}\)the graph is hyperbola.

Step-by-step solution

Graph of the given question.

Above the graph definition.

The graph is parabola\({\rm{d}} \ne {\rm{0}}\).

\({\rm{d < 0}}\)is Parabola concave down

\({\rm{d < 0}}\)is Parabola concave up.

Therefore, x- Intercepts increases with the magnitude of d.

The shape of conic.

Above the graph definition.

\({\rm{e < 0}}\)the graph is ellipse.

\({\rm{e = 1}}\)the graph is parabola.

\({\rm{e > 0}}\)the graph is hyperbola.