How do you write the equation for a circle with points (0, 2a) (2b, 0) as ends of a diameter?

1 Answer
Jan 22, 2017

Answer:

The x coordinate goes from 0 to 2b so the center is at b. Likewise, the y coordinate goes from 2a to 0 so the center is at a.
Use the equation #(x-h)^2+(y-k)^2=r^2; h=b,k=a# and one of the points.

Explanation:

Use the equation
#(x-h)^2+(y-k)^2=r^2#

where #h=b and k=a#

#(x - b)^2 + (y - a)^2 = r^2#

Let's use the point #(0,2a)#, to find the value of r:

#(0 - b)^2 + (2a - a)^2 = r^2#

#r^2 = a^2 + b^2#

#r = sqrt(a^2 + b^2)#

Here is the equation of the circle:

#(x - b)^2 + (y - a)^2 = (sqrt(a^2 + b^2))^2#