# Category:Polars of Points

This category contains results about Polars of Points.

Definitions specific to this category can be found in Definitions/Polars of Points.

### Circle

Let $\CC$ be a circle whose radius is $r$ and whose center is at the origin of a Cartesian plane.

Let $P = \tuple {x_0, y_0}$ be an arbitrary point in the Cartesian plane.

The **polar of $P$ with respect to $\CC$** is the straight line whose equation is given by:

- $x x_0 + y y_0 = r^2$

### Ellipse

Let $\EE$ be an ellipse embedded in a Cartesian plane in reduced form with the equation:

- $\dfrac {x^2} {a^2} + \dfrac {y^2} {b^2} = 1$

Let $P = \tuple {x_0, y_0}$ be an arbitrary point in the Cartesian plane.

The **polar of $P$ with respect to $\EE$** is the straight line whose equation is given by:

- $\dfrac {x x_0} {a^2} + \dfrac {y y_0} {b^2} = 1$

## Subcategories

This category has the following 5 subcategories, out of 5 total.

### C

- Chords of Contact (2 P)
- Conjugate Lines (3 P)
- Conjugate Points (2 P)
- Conjugate Triangles (4 P)

### H

## Pages in category "Polars of Points"

The following 8 pages are in this category, out of 8 total.