# Conic Sections in Polar Coordinates

(a)

Also, we have (1)

Pl is parallel to the x-axis, so Pl = DE (2)

And (3)

Substitute (2) and (3) to equation (1), we have

Therefore,

Then PF = r

According to the definition of e, we have , so

(*)

The conversion between the polar and rectangular coordinates is

(4)

Therefore, (5)

Square both sides of equation (*), we have

(6)

Substitute equations (4) and (5) to (6)

(7)

When e <1, , so , that is, the coefficient of is greater than 0. so it is an equation of ellipse.

When e > 1, , equation (7) is

, so it is an equation of hyperbola.

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4. The conversion between the polar and rectangular coordinates is

(1)

Therefore, (2)

Given that:

Cross-multiplying,

r + r e cos = ed, or r = ...

#### Solution Summary

Conic Sections in Polar Coordinates are investigated.