Find the equation of a circle, the co-ordinates of the ends of whose diameter are `(-1,-3) and (2,5)`
Now the equation of circle
`(x-x_(1))(x-x_(2))+(y-y_(1))(y-y_(2))=0`
`rArr(x+1)(x-2)+(y+3)(y-5)=0`
`rArr x^(2)-x-2+ y^(2)-2y-15=0`
`rArr x^(2)+y^(2)-x-2y-17=0`
We is the required equation.

Explanation

Here `(x_(1),y_(1))=(-1,-3) and (x_(2),y_(2))=(2,5)`
Now the equation of circle
`(x-x_(1))(x-x_(2))+(y-y_(1))(y-y_(2))=0`
`rArr(x+1)(x-2)+(y+3)(y-5)=0`
`rArr x^(2)-x-2+ y^(2)-2y-15=0`
`rArr x^(2)+y^(2)-x-2y-17=0`
which is the required equation.