Find the equation of the circle the end points of whose diameters are the centres of the circles `x^2+y^2+16x-14y=1` and `x^2+y^2-4x+10y=2`

Explanation

`x^{2}+y^{2}+16 x-14 y-1=0 ldots .(1)` (given)


Centre` =[(-16 / 2),-(-14 / 2)]`


`=[-8,7] `


`x^{2}+y^{2}-4 x+10 y-2=0 ldots (2)` (given)


Centre` =[-(-4 / 2),(-10 / 2)]`


`=[2,-5]`


The equation of the circle is


`(x-x_{1})(x-x_{2})+(y-y_{1})(y-y_{2})=0`


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