Answer :
To convert the given polar equation to an equivalent rectangular equation, we start by examining the given:
[tex]r = 13[/tex]
In polar coordinates, [tex]r[/tex] represents the distance from the origin to a point [tex](r, \theta)[/tex] in the plane. In rectangular coordinates, [tex]r[/tex] can be expressed as:
[tex]r = \sqrt{x^2 + y^2}[/tex]
To convert this polar equation into a rectangular one, we substitute [tex]r[/tex] with [tex]\sqrt{x^2 + y^2}[/tex]:
[tex]\sqrt{x^2 + y^2} = 13[/tex]
To eliminate the square root, square both sides of the equation:
[tex]x^2 + y^2 = 169[/tex]
This is the equation of a circle with a center at the origin (0, 0) and a radius of 13 in the rectangular (Cartesian) coordinate system.
Let's summarize:
The original polar equation is [tex]r = 13[/tex].
The equivalent rectangular equation, after substituting and simplifying, is [tex]x^2 + y^2 = 169[/tex].
Thus, the rectangular equation represents a circle centered at the origin with a radius of 13 units.
