Find the equation of circle having x-y-2=0 and x-y+2=0 as two tangents and x-y=0as diameter?(ans is x² + y² =2)how??????

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Dear   arzoo

given tangent line and diameter line are parallel to each other

radius is equal to distance between ant tangent line and diameter line that is equal to = √2

and center of line lie on the line the diameter line/

let co ordinate of center is (h,k)

since this lie on line x-y=0

so h=k

so equation of circle  (x-h)² +( y-h)² =2

it is a family of circle one of the possible circle is for h=0

 x² + y² =2

similerly you will get many nore circle for different value of h

I think equation of diameter line should be x+y=0

then you will onle one circle  x² + y² =2