Question

how would you find an equation for a circle that passes through the origin and has intercepts equal to 1 and 2 on the x and y axes

Answer 1

The general equation for a circle is:

(x-a)^2 + (y-b)^2 = R^2

R is the radius of the circle and the point (a,b) is the center. To solve the problem you just insert the coordinates of the three points that are known to be on the circle in the equation and solve for a, b and R:


Origin: x = 0, y = 0:

a^2 + b^2 = R^2

x= 1, y= 0:

(1-a)^2 +b^2 = R^2

x= 0, y= 2:


a^2 + (2-b)^2 = R^2

Subtract from the last two equations the first equation to obtain two equations one containing only a and the other containing only b.

Answer 2

ok so i found:

(y-1)^2 + (x-.5)^2 - r^2
so how do you find r??