Question

How do you graph `r=(23)/(7-5sin theta)`?

Answer 1

See Socratic graph and explanation.

Explanation:

Use `l/r = 1 + e cos (theta-alpha)`, with e < 1, represents an ellipse

with a focus at the pole (0, 0) and major axis along `theta = alpha`,

The semi major axis `a = l / (1-e^2)`.

This can be reorganized to the form

`(23/7)/r=1+5/7cos (theta+pi/2)` revealing that the graph is the

ellipse with a focus S(0, 0). e = 5/7, `alpha = -pi/2` , a =

161/24 = 6.71, nearly, and .

semi minor axis

`b = sqrt (la) = sqrt((23/7)(161/24)) = 23/sqrt (24)` = 4.7, nearly.

A short Table for tracing the ellipse.

`(r, theta)`:

`(0, 23/7) (46/9, pi/6) ( 23/2, pi/2) (46/9, 5/6pi) (23/7, pi)`

`(46/19, 7/6pi) (23/12, 3/2pi) (46/19, 11/6pi) (23/7, 2pi)`

See a Socratic graph. Note that the major axis ( length 13.42 ) is

along y-axis.

graph{(x^2+y^2)^0.5-23/7 -5/7 y=0[-10 10 -3 12]}