Answer to Question #137725 in Analytic Geometry for Chaz Guerrero-Bartlett

Question

The equation of a circle is x2 + y2 = 29.

Determine which point lies on the circle.

Answer 1

$x^2 + y^2 = 29\\ (x - 0)^2 + (y - 0)^2 = (\sqrt{29})^2\\ \textsf{The equation describes a circle of radius}\\ \sqrt{29}\hspace{0.1cm} \textsf{units centered at the origin.}\\ \textsf{There are infinitely many points which lie on the circle}\\\textsf{within the end points of the circle,}\\\textsf{but no points outside this range}\\\textsf{lie on the circle}\\ \textsf{In general, any point which lies on}\\\textsf{the circle should be a part of the set}\hspace{0.1cm} \{(x,y): x \in [-\sqrt{29}, \sqrt{29}], y \in [-\sqrt{29}, \sqrt{29}]\}.$