Find the equation of the circle drawn on the intercept made by the line `2x+3y=6` between the coordinate axes as diameter.

Explanation

Given `2x+3y=6`

`implies \frac{x}{3}+\frac{y}{2}=1`

Then the line` 2x+3y=6` meets x and y-axes at `P(3,0)` and `Q(0,2)` respectively.

Now taking `PQ` as a diameter of the circle, then the required equation of the circle is :

`(x−3)(x−0)+(y−0)(y−2)=0`

`impliesx^2+y^2−3x−2y=0`

Hence, the equation of circle is `x^2+y^2−3x−2y=0`