Question

What is the standard form of the equation of a circle with center at (3, 2) and through the point (5, 4)?

Answer 1

`(x-3)^2 + (y-2)^2 = 8`

Explanation:

The standard form of the equation of a circle is :

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

where (a , b ) are the coords of centre and r , the radius.

Here the centre is known but require to find radius. This can be done using the 2 coord points given.

using the`color(blue)" distance formula "`

`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`

let`(x_1,y_1)=(3,2)" and "(x_2,y_2)= (5,4)`

`d = r =sqrt((5-3)^2 + (4-2)^2) = sqrt8`

equation of circle is `: (x-3)^2 + (y-2)^2 = (sqrt8)^2`