Question

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

Answer 1

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`