Question

How do you derive the equation of a circle?

Answer 1

please you have to start from the definition of a circle:
" A circle is a curve wherein the distance between each point, which belong to such circle, and another point, which is the centre of such circle, is equal to the radius of such circle"

Answer 2

draw a circle on a graph with known center (not the origon) and known radius
Then take any point on the graph (x,y). Use cordinate geometry and pythagoras theorem to find a relation between x and y .

Answer 3

now we can implement such definition, using the cartesian coordinates, and the euclidean distance between two points, like below:
\[\Large \sqrt {{{\left( {x - {x_0}} \right)}^2} + {{\left( {y - {y_0}} \right)}^2}} = r\]

Answer 4

thank you both (: this is a great explanation

Answer 5

:)

Answer 6

yw