How do you graph polar curves to see the points of intersection of the curves?

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How do you graph polar curves to see the points of intersection of the curves?

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Answer 1 · 2016-05-18T02:40:01

If the polar equations are $r = f(theta) and r = g(theta)$ or, inversely, $theta = f^(-1)(r) and theta = g^(-1)(r)$ . eliminate either r or $theta$ , solve and substitute in one of the equations..

Explanation:

Explication:

Find the points of intersection of the cardioid

$r = a( 1 + cos theta )$ and the circle r = a.

Eliminate r.

The equation for $theta$ at a point of intersection is

$a = a(1+cos theta)$ . this is #cos theta = 0 rarr theta = pi/2 and

(3pi)/2#.

The common points are $(a, pi/2) and (a, (3pi)/2)$

For the graph, a = 1. Use $(x, y) = r(cos theta, sin theta)$

graph{(x^2+y^2-(x^2+y^2)^0.5-x)(x^2+y^2-1)=0[-2 4 -1.5 1.5]}

The two parabolas $1 = r (1 + cos theta) and 1 = r(1 - cos theta)$

intersect at $(1, pi/2)$ and $(1, 3pi/2)$ .
graph{(x+(x^2+y^2)^0.5-1)(-x+(x^2+y^2)^0.5-1)=0[-3 3 -1.5 1.5]}

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How do you graph polar curves to see the points of intersection of the curves?

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